Linear models

Andrew Irwin, a.irwin@dal.ca

2024-02-13

Linear models

  • Describing, fitting, and using models

  • Linear regression

    • Straight lines
    • Polynomials
    • log transforms

  • Quantile regression

  • Accessing model coefficients

  • Calculating residuals

  • Making predictions: point estimates and standard errors or confidence intervals

Start with a basic graph

Fit a straight line

m1 <- lm( city_l100km ~ displ, data = my_mpg)
summary(m1)

Call:
lm(formula = city_l100km ~ displ, data = my_mpg)

Residuals:
    Min      1Q  Median      3Q     Max 
-7.4102 -1.1345 -0.1942  0.9745  8.4218 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   6.7233     0.4204   15.99   <2e-16 ***
displ         2.3383     0.1135   20.60   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.239 on 232 degrees of freedom
Multiple R-squared:  0.6465,    Adjusted R-squared:  0.645 
F-statistic: 424.3 on 1 and 232 DF,  p-value: < 2.2e-16

Fit a straight line

library(broom)
glance(m1)  |> kable(digits = 2) |> kable_styling(full_width = FALSE)
r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC deviance df.residual nobs
0.65 0.65 2.24 424.35 0 1 -519.59 1045.18 1055.54 1162.55 232 234 
tidy(m1) |> kable(digits = 2) |> kable_styling(full_width = FALSE)
term estimate std.error statistic p.value
(Intercept) 6.72 0.42 15.99 0
displ 2.34 0.11 20.60 0

Graph estimated terms

tidy(m1, conf.int = TRUE) |>
  ggplot(aes(y = term, x = estimate, xmin = conf.low, xmax = conf.high)) + 
  geom_pointrange() + my_theme

Polynomial regression

m2 <- lm( city_l100km ~ poly(displ,2), data = my_mpg)
glance(m2) |> kable(digits = 2) |> kable_styling(full_width = FALSE)
r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC deviance df.residual nobs
0.68 0.68 2.13 246.38 0 2 -507.64 1023.29 1037.11 1049.71 231 234 
tidy(m2) |> kable(digits = 2) |> kable_styling(full_width = FALSE)
term estimate std.error statistic p.value
(Intercept) 14.84 0.14 106.50 0
poly(displ, 2)1 46.11 2.13 21.63 0
poly(displ, 2)2 -10.62 2.13 -4.98 0

Log transforms

gapminder |> ggplot(aes(x = gdpPercap, y= lifeExp)) + geom_point() +
  scale_x_log10() + 
   geom_smooth(method = "lm", formula = y ~ x) + my_theme

Log transforms

m3 <- gapminder |> mutate(logGDPpercap = log10(gdpPercap)) %>%
  lm( lifeExp ~ logGDPpercap, data = . ) 
tidy(m3) |> kable(digits = 2) |> kable_styling(full_width = FALSE)
term estimate std.error statistic p.value
(Intercept) -9.10 1.23 -7.41 0
logGDPpercap 19.35 0.34 56.50 0 
glance(m3) |> kable(digits = 2) |> kable_styling(full_width = FALSE)
r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC deviance df.residual nobs
0.65 0.65 7.62 3192.27 0 1 -5877.21 11760.42 11776.74 98813.56 1702 1704

Alternative: two step

d3 <- gapminder |> mutate(logGDPpercap = log10(gdpPercap))
m3 <- lm( lifeExp ~ logGDPpercap, data = d3 ) 
tidy(m3) |> kable(digits = 2) |> kable_styling(full_width = FALSE)
term estimate std.error statistic p.value
(Intercept) -9.10 1.23 -7.41 0
logGDPpercap 19.35 0.34 56.50 0

Quantile regression

library(quantreg)
m4 <- rq(city_l100km ~ displ, data = my_mpg,
                      tau = 0.50) # quantile, between 0 and 1
tidy(m4) |> kable(digits = 2)
term estimate conf.low conf.high tau
(Intercept) 6.26 5.2 7.10 0.5
displ 2.47 2.0 3.03 0.5 
glance(m4) |> kable(digits = 2)
tau logLik AIC BIC df.residual
0.5 -497.0873 998.17 1005.09 232

Working with models: predictions

predict(m1, se.fit = TRUE) |> kable(digits = 2) # confusing!
x
10.93
10.93
11.40
11.40
13.27
13.27
13.97
10.93
10.93
11.40
11.40
13.27
13.27
13.97
13.97
13.27
13.97
16.54
19.12
19.12
19.12
20.05
20.75
20.05
20.05
21.22
21.22
23.09
19.12
19.12
20.05
21.92
12.34
12.34
13.97
14.91
15.14
12.34
13.74
14.44
14.44
14.44
14.44
14.44
15.61
15.61
15.61
16.08
15.37
15.37
15.84
15.84
17.71
17.71
17.71
18.88
18.88
15.84
17.71
17.71
17.71
18.88
20.05
20.52
17.71
17.71
17.71
17.71
17.71
17.71
18.88
18.88
20.05
20.52
17.48
19.35
19.35
16.08
16.08
16.08
16.08
17.48
18.41
16.54
16.54
17.48
17.48
17.48
19.35
19.35
15.61
15.61
16.08
16.08
17.48
17.48
17.48
17.48
19.35
10.46
10.46
10.46
10.46
10.46
10.93
10.93
10.93
11.40
12.34
12.34
12.34
12.34
12.57
12.57
14.44
11.40
11.40
11.40
11.40
13.04
13.04
13.04
13.74
15.37
16.08
17.71
17.71
17.71
20.05
20.99
16.08
16.54
17.01
17.48
19.35
19.35
19.35
16.08
16.08
17.48
18.41
12.34
12.34
12.57
12.57
14.91
14.91
13.74
13.74
14.91
14.44
14.44
16.08
19.82
13.97
15.61
15.61
15.61
19.12
12.57
12.57
12.57
12.57
12.57
12.57
11.87
11.87
12.57
12.57
12.57
12.57
12.57
12.57
13.04
13.04
14.67
14.67
16.08
17.71
11.87
11.87
12.34
12.34
13.74
13.74
14.91
11.87
11.87
12.34
12.34
13.74
13.74
14.44
10.93
10.93
10.93
10.93
10.93
17.71
20.05
13.04
13.04
13.04
14.67
14.67
16.08
16.08
11.40
11.40
11.40
11.40
13.27
11.17
11.40
11.40
11.40
11.40
12.57
12.57
13.27
13.27
11.17
11.17
11.40
11.40
12.57
12.57
10.93
10.93
11.40
11.40
13.27
13.27
15.14
x
0.24
0.24
0.22
0.22
0.17
0.17
0.15
0.24
0.24
0.22
0.22
0.17
0.17
0.15
0.15
0.17
0.15
0.17
0.25
0.25
0.25
0.29
0.32
0.29
0.29
0.34
0.34
0.43
0.25
0.25
0.29
0.37
0.19
0.19
0.15
0.15
0.15
0.19
0.16
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.15
0.16
0.15
0.15
0.15
0.15
0.20
0.20
0.20
0.24
0.24
0.15
0.20
0.20
0.20
0.24
0.29
0.31
0.20
0.20
0.20
0.20
0.20
0.20
0.24
0.24
0.29
0.31
0.19
0.26
0.26
0.16
0.16
0.16
0.16
0.19
0.23
0.17
0.17
0.19
0.19
0.19
0.26
0.26
0.15
0.15
0.16
0.16
0.19
0.19
0.19
0.19
0.26
0.26
0.26
0.26
0.26
0.26
0.24
0.24
0.24
0.22
0.19
0.19
0.19
0.19
0.18
0.18
0.15
0.22
0.22
0.22
0.22
0.17
0.17
0.17
0.16
0.15
0.16
0.20
0.20
0.20
0.29
0.33
0.16
0.17
0.18
0.19
0.26
0.26
0.26
0.16
0.16
0.19
0.23
0.19
0.19
0.18
0.18
0.15
0.15
0.16
0.16
0.15
0.15
0.15
0.16
0.28
0.15
0.15
0.15
0.15
0.25
0.18
0.18
0.18
0.18
0.18
0.18
0.21
0.21
0.18
0.18
0.18
0.18
0.18
0.18
0.17
0.17
0.15
0.15
0.16
0.20
0.21
0.21
0.19
0.19
0.16
0.16
0.15
0.21
0.21
0.19
0.19
0.16
0.16
0.15
0.24
0.24
0.24
0.24
0.24
0.20
0.29
0.17
0.17
0.17
0.15
0.15
0.16
0.16
0.22
0.22
0.22
0.22
0.17
0.23
0.22
0.22
0.22
0.22
0.18
0.18
0.17
0.17
0.23
0.23
0.22
0.22
0.18
0.18
0.24
0.24
0.22
0.22
0.17
0.17
0.15
x
232
x
2.24

Working with models: residuals

residuals(m1) |> as_tibble() |> kable(digits = 2)
value
2.14
0.27
0.36
-0.20
1.43
-0.20
-0.90
2.14
3.77
0.36
0.98
2.41
0.57
-0.14
1.71
2.41
-0.14
-1.84
-2.32
2.27
-2.32
-1.96
-1.15
-5.35
-4.37
-6.52
-5.54
-7.41
-2.32
2.27
1.33
-5.12
0.04
-1.64
-0.90
-1.84
-1.30
0.73
0.10
0.26
0.26
-0.60
-0.60
6.94
0.07
0.07
-0.91
-1.38
0.31
1.43
2.25
0.96
-0.91
-0.91
8.42
2.50
2.50
2.25
0.38
8.42
0.38
2.50
-1.96
0.86
1.89
8.42
0.38
0.38
1.89
8.42
2.50
2.50
-1.96
0.86
3.90
2.03
0.25
0.72
-0.40
0.72
2.02
0.61
-0.32
0.26
0.26
0.61
0.61
0.61
2.03
-1.26
-2.54
-2.54
-2.24
-1.38
-1.80
-1.80
-1.80
-1.80
-2.55
-2.06
-0.66
-1.06
-0.24
-0.66
-1.89
-1.52
-1.13
-0.20
0.73
0.73
-1.13
-1.13
0.50
0.50
-2.06
0.98
0.98
0.36
0.36
0.80
1.66
0.80
0.10
0.31
-0.40
-0.91
8.42
-0.91
-1.96
0.40
5.31
3.06
2.59
3.90
2.03
2.03
0.25
0.72
2.02
0.61
-0.32
-1.13
0.04
-2.34
-2.34
-2.53
-2.53
-0.67
-1.36
-2.53
2.36
1.24
0.72
-0.22
-0.90
-0.91
-1.77
-2.54
-4.42
0.50
0.50
-0.81
-0.19
-0.81
0.50
-0.67
0.51
-0.19
-0.19
-0.81
-0.81
-0.19
-0.81
2.64
1.66
1.01
1.01
-1.38
-0.91
-0.67
-0.67
-1.13
-1.13
-0.67
-0.67
-2.53
-0.67
-0.67
-1.13
-1.64
-0.67
-0.67
-1.37
-1.13
-1.13
-1.89
-2.53
-1.89
3.67
-1.96
2.64
1.66
0.80
1.01
1.01
-0.40
-1.38
-0.20
0.98
-0.20
-0.71
0.57
-4.04
-0.20
0.98
-0.71
-0.20
-1.37
-1.37
1.43
0.57
-4.45
-3.06
-0.20
0.98
-0.81
-0.81
0.27
2.14
0.98
-0.20
1.43
-0.20
-1.30

Combining with original data

bind_cols(my_mpg |> select(displ, city_l100km),
          predict(m1) |> as_tibble() |> rename(predict = value),
          residuals(m1) |> as_tibble() |> rename(residual = value)) |> kable(digits = 2)
displ city_l100km predict residual
1.8 13.07 10.93 2.14
1.8 11.20 10.93 0.27
2.0 11.76 11.40 0.36
2.0 11.20 11.40 -0.20
2.8 14.70 13.27 1.43
2.8 13.07 13.27 -0.20
3.1 13.07 13.97 -0.90
1.8 13.07 10.93 2.14
1.8 14.70 10.93 3.77
2.0 11.76 11.40 0.36
2.0 12.38 11.40 0.98
2.8 15.68 13.27 2.41
2.8 13.84 13.27 0.57
3.1 13.84 13.97 -0.14
3.1 15.68 13.97 1.71
2.8 15.68 13.27 2.41
3.1 13.84 13.97 -0.14
4.2 14.70 16.54 -1.84
5.3 16.80 19.12 -2.32
5.3 21.38 19.12 2.27
5.3 16.80 19.12 -2.32
5.7 18.09 20.05 -1.96
6.0 19.60 20.75 -1.15
5.7 14.70 20.05 -5.35
5.7 15.68 20.05 -4.37
6.2 14.70 21.22 -6.52
6.2 15.68 21.22 -5.54
7.0 15.68 23.09 -7.41
5.3 16.80 19.12 -2.32
5.3 21.38 19.12 2.27
5.7 21.38 20.05 1.33
6.5 16.80 21.92 -5.12
2.4 12.38 12.34 0.04
2.4 10.69 12.34 -1.64
3.1 13.07 13.97 -0.90
3.5 13.07 14.91 -1.84
3.6 13.84 15.14 -1.30
2.4 13.07 12.34 0.73
3.0 13.84 13.74 0.10
3.3 14.70 14.44 0.26
3.3 14.70 14.44 0.26
3.3 13.84 14.44 -0.60
3.3 13.84 14.44 -0.60
3.3 21.38 14.44 6.94
3.8 15.68 15.61 0.07
3.8 15.68 15.61 0.07
3.8 14.70 15.61 -0.91
4.0 14.70 16.08 -1.38
3.7 15.68 15.37 0.31
3.7 16.80 15.37 1.43
3.9 18.09 15.84 2.25
3.9 16.80 15.84 0.96
4.7 16.80 17.71 -0.91
4.7 16.80 17.71 -0.91
4.7 26.13 17.71 8.42
5.2 21.38 18.88 2.50
5.2 21.38 18.88 2.50
3.9 18.09 15.84 2.25
4.7 18.09 17.71 0.38
4.7 26.13 17.71 8.42
4.7 18.09 17.71 0.38
5.2 21.38 18.88 2.50
5.7 18.09 20.05 -1.96
5.9 21.38 20.52 0.86
4.7 19.60 17.71 1.89
4.7 26.13 17.71 8.42
4.7 18.09 17.71 0.38
4.7 18.09 17.71 0.38
4.7 19.60 17.71 1.89
4.7 26.13 17.71 8.42
5.2 21.38 18.88 2.50
5.2 21.38 18.88 2.50
5.7 18.09 20.05 -1.96
5.9 21.38 20.52 0.86
4.6 21.38 17.48 3.90
5.4 21.38 19.35 2.03
5.4 19.60 19.35 0.25
4.0 16.80 16.08 0.72
4.0 15.68 16.08 -0.40
4.0 16.80 16.08 0.72
4.0 18.09 16.08 2.02
4.6 18.09 17.48 0.61
5.0 18.09 18.41 -0.32
4.2 16.80 16.54 0.26
4.2 16.80 16.54 0.26
4.6 18.09 17.48 0.61
4.6 18.09 17.48 0.61
4.6 18.09 17.48 0.61
5.4 21.38 19.35 2.03
5.4 18.09 19.35 -1.26
3.8 13.07 15.61 -2.54
3.8 13.07 15.61 -2.54
4.0 13.84 16.08 -2.24
4.0 14.70 16.08 -1.38
4.6 15.68 17.48 -1.80
4.6 15.68 17.48 -1.80
4.6 15.68 17.48 -1.80
4.6 15.68 17.48 -1.80
5.4 16.80 19.35 -2.55
1.6 8.40 10.46 -2.06
1.6 9.80 10.46 -0.66
1.6 9.41 10.46 -1.06
1.6 10.23 10.46 -0.24
1.6 9.80 10.46 -0.66
1.8 9.05 10.93 -1.89
1.8 9.41 10.93 -1.52
1.8 9.80 10.93 -1.13
2.0 11.20 11.40 -0.20
2.4 13.07 12.34 0.73
2.4 13.07 12.34 0.73
2.4 11.20 12.34 -1.13
2.4 11.20 12.34 -1.13
2.5 13.07 12.57 0.50
2.5 13.07 12.57 0.50
3.3 12.38 14.44 -2.06
2.0 12.38 11.40 0.98
2.0 12.38 11.40 0.98
2.0 11.76 11.40 0.36
2.0 11.76 11.40 0.36
2.7 13.84 13.04 0.80
2.7 14.70 13.04 1.66
2.7 13.84 13.04 0.80
3.0 13.84 13.74 0.10
3.7 15.68 15.37 0.31
4.0 15.68 16.08 -0.40
4.7 16.80 17.71 -0.91
4.7 26.13 17.71 8.42
4.7 16.80 17.71 -0.91
5.7 18.09 20.05 -1.96
6.1 21.38 20.99 0.40
4.0 21.38 16.08 5.31
4.2 19.60 16.54 3.06
4.4 19.60 17.01 2.59
4.6 21.38 17.48 3.90
5.4 21.38 19.35 2.03
5.4 21.38 19.35 2.03
5.4 19.60 19.35 0.25
4.0 16.80 16.08 0.72
4.0 18.09 16.08 2.02
4.6 18.09 17.48 0.61
5.0 18.09 18.41 -0.32
2.4 11.20 12.34 -1.13
2.4 12.38 12.34 0.04
2.5 10.23 12.57 -2.34
2.5 10.23 12.57 -2.34
3.5 12.38 14.91 -2.53
3.5 12.38 14.91 -2.53
3.0 13.07 13.74 -0.67
3.0 12.38 13.74 -1.36
3.5 12.38 14.91 -2.53
3.3 16.80 14.44 2.36
3.3 15.68 14.44 1.24
4.0 16.80 16.08 0.72
5.6 19.60 19.82 -0.22
3.1 13.07 13.97 -0.90
3.8 14.70 15.61 -0.91
3.8 13.84 15.61 -1.77
3.8 13.07 15.61 -2.54
5.3 14.70 19.12 -4.42
2.5 13.07 12.57 0.50
2.5 13.07 12.57 0.50
2.5 11.76 12.57 -0.81
2.5 12.38 12.57 -0.19
2.5 11.76 12.57 -0.81
2.5 13.07 12.57 0.50
2.2 11.20 11.87 -0.67
2.2 12.38 11.87 0.51
2.5 12.38 12.57 -0.19
2.5 12.38 12.57 -0.19
2.5 11.76 12.57 -0.81
2.5 11.76 12.57 -0.81
2.5 12.38 12.57 -0.19
2.5 11.76 12.57 -0.81
2.7 15.68 13.04 2.64
2.7 14.70 13.04 1.66
3.4 15.68 14.67 1.01
3.4 15.68 14.67 1.01
4.0 14.70 16.08 -1.38
4.7 16.80 17.71 -0.91
2.2 11.20 11.87 -0.67
2.2 11.20 11.87 -0.67
2.4 11.20 12.34 -1.13
2.4 11.20 12.34 -1.13
3.0 13.07 13.74 -0.67
3.0 13.07 13.74 -0.67
3.5 12.38 14.91 -2.53
2.2 11.20 11.87 -0.67
2.2 11.20 11.87 -0.67
2.4 11.20 12.34 -1.13
2.4 10.69 12.34 -1.64
3.0 13.07 13.74 -0.67
3.0 13.07 13.74 -0.67
3.3 13.07 14.44 -1.37
1.8 9.80 10.93 -1.13
1.8 9.80 10.93 -1.13
1.8 9.05 10.93 -1.89
1.8 8.40 10.93 -2.53
1.8 9.05 10.93 -1.89
4.7 21.38 17.71 3.67
5.7 18.09 20.05 -1.96
2.7 15.68 13.04 2.64
2.7 14.70 13.04 1.66
2.7 13.84 13.04 0.80
3.4 15.68 14.67 1.01
3.4 15.68 14.67 1.01
4.0 15.68 16.08 -0.40
4.0 14.70 16.08 -1.38
2.0 11.20 11.40 -0.20
2.0 12.38 11.40 0.98
2.0 11.20 11.40 -0.20
2.0 10.69 11.40 -0.71
2.8 13.84 13.27 0.57
1.9 7.13 11.17 -4.04
2.0 11.20 11.40 -0.20
2.0 12.38 11.40 0.98
2.0 10.69 11.40 -0.71
2.0 11.20 11.40 -0.20
2.5 11.20 12.57 -1.37
2.5 11.20 12.57 -1.37
2.8 14.70 13.27 1.43
2.8 13.84 13.27 0.57
1.9 6.72 11.17 -4.45
1.9 8.11 11.17 -3.06
2.0 11.20 11.40 -0.20
2.0 12.38 11.40 0.98
2.5 11.76 12.57 -0.81
2.5 11.76 12.57 -0.81
1.8 11.20 10.93 0.27
1.8 13.07 10.93 2.14
2.0 12.38 11.40 0.98
2.0 11.20 11.40 -0.20
2.8 14.70 13.27 1.43
2.8 13.07 13.27 -0.20
3.6 13.84 15.14 -1.30

Predictions from new data

new_data = tibble(displ = seq(1.6, 7.2, by = 0.5))
new_data |> mutate(prediction = predict(m1, new_data)) |> kable(digits = 2)
displ prediction
1.6 10.46
2.1 11.63
2.6 12.80
3.1 13.97
3.6 15.14
4.1 16.31
4.6 17.48
5.1 18.65
5.6 19.82
6.1 20.99
6.6 22.16
7.1 23.33

Model uncertainties

bind_cols(my_mpg |>  select(displ, city_l100km),
          predict(m1, se.fit = TRUE) |> as_tibble() ) |>
 distinct() |> kable(digits = 2)
displ city_l100km fit se.fit df residual.scale
1.8 13.07 10.93 0.24 232 2.24
1.8 11.20 10.93 0.24 232 2.24
2.0 11.76 11.40 0.22 232 2.24
2.0 11.20 11.40 0.22 232 2.24
2.8 14.70 13.27 0.17 232 2.24
2.8 13.07 13.27 0.17 232 2.24
3.1 13.07 13.97 0.15 232 2.24
1.8 13.07 10.93 0.24 232 2.24
1.8 14.70 10.93 0.24 232 2.24
2.0 12.38 11.40 0.22 232 2.24
2.8 15.68 13.27 0.17 232 2.24
2.8 13.84 13.27 0.17 232 2.24
3.1 13.84 13.97 0.15 232 2.24
3.1 15.68 13.97 0.15 232 2.24
4.2 14.70 16.54 0.17 232 2.24
5.3 16.80 19.12 0.25 232 2.24
5.3 21.38 19.12 0.25 232 2.24
5.7 18.09 20.05 0.29 232 2.24
6.0 19.60 20.75 0.32 232 2.24
5.7 14.70 20.05 0.29 232 2.24
5.7 15.68 20.05 0.29 232 2.24
6.2 14.70 21.22 0.34 232 2.24
6.2 15.68 21.22 0.34 232 2.24
7.0 15.68 23.09 0.43 232 2.24
5.7 21.38 20.05 0.29 232 2.24
6.5 16.80 21.92 0.37 232 2.24
2.4 12.38 12.34 0.19 232 2.24
2.4 10.69 12.34 0.19 232 2.24
3.5 13.07 14.91 0.15 232 2.24
3.6 13.84 15.14 0.15 232 2.24
2.4 13.07 12.34 0.19 232 2.24
3.0 13.84 13.74 0.16 232 2.24
3.3 14.70 14.44 0.15 232 2.24
3.3 13.84 14.44 0.15 232 2.24
3.3 21.38 14.44 0.15 232 2.24
3.8 15.68 15.61 0.15 232 2.24
3.8 14.70 15.61 0.15 232 2.24
4.0 14.70 16.08 0.16 232 2.24
3.7 15.68 15.37 0.15 232 2.24
3.7 16.80 15.37 0.15 232 2.24
3.9 18.09 15.84 0.15 232 2.24
3.9 16.80 15.84 0.15 232 2.24
4.7 16.80 17.71 0.20 232 2.24
4.7 26.13 17.71 0.20 232 2.24
5.2 21.38 18.88 0.24 232 2.24
4.7 18.09 17.71 0.20 232 2.24
5.9 21.38 20.52 0.31 232 2.24
4.7 19.60 17.71 0.20 232 2.24
4.6 21.38 17.48 0.19 232 2.24
5.4 21.38 19.35 0.26 232 2.24
5.4 19.60 19.35 0.26 232 2.24
4.0 16.80 16.08 0.16 232 2.24
4.0 15.68 16.08 0.16 232 2.24
4.0 18.09 16.08 0.16 232 2.24
4.6 18.09 17.48 0.19 232 2.24
5.0 18.09 18.41 0.23 232 2.24
4.2 16.80 16.54 0.17 232 2.24
5.4 18.09 19.35 0.26 232 2.24
3.8 13.07 15.61 0.15 232 2.24
4.0 13.84 16.08 0.16 232 2.24
4.6 15.68 17.48 0.19 232 2.24
5.4 16.80 19.35 0.26 232 2.24
1.6 8.40 10.46 0.26 232 2.24
1.6 9.80 10.46 0.26 232 2.24
1.6 9.41 10.46 0.26 232 2.24
1.6 10.23 10.46 0.26 232 2.24
1.8 9.05 10.93 0.24 232 2.24
1.8 9.41 10.93 0.24 232 2.24
1.8 9.80 10.93 0.24 232 2.24
2.4 11.20 12.34 0.19 232 2.24
2.5 13.07 12.57 0.18 232 2.24
3.3 12.38 14.44 0.15 232 2.24
2.7 13.84 13.04 0.17 232 2.24
2.7 14.70 13.04 0.17 232 2.24
6.1 21.38 20.99 0.33 232 2.24
4.0 21.38 16.08 0.16 232 2.24
4.2 19.60 16.54 0.17 232 2.24
4.4 19.60 17.01 0.18 232 2.24
2.5 10.23 12.57 0.18 232 2.24
3.5 12.38 14.91 0.15 232 2.24
3.0 13.07 13.74 0.16 232 2.24
3.0 12.38 13.74 0.16 232 2.24
3.3 16.80 14.44 0.15 232 2.24
3.3 15.68 14.44 0.15 232 2.24
5.6 19.60 19.82 0.28 232 2.24
3.8 13.84 15.61 0.15 232 2.24
5.3 14.70 19.12 0.25 232 2.24
2.5 11.76 12.57 0.18 232 2.24
2.5 12.38 12.57 0.18 232 2.24
2.2 11.20 11.87 0.21 232 2.24
2.2 12.38 11.87 0.21 232 2.24
2.7 15.68 13.04 0.17 232 2.24
3.4 15.68 14.67 0.15 232 2.24
3.3 13.07 14.44 0.15 232 2.24
1.8 8.40 10.93 0.24 232 2.24
4.7 21.38 17.71 0.20 232 2.24
2.0 10.69 11.40 0.22 232 2.24
1.9 7.13 11.17 0.23 232 2.24
2.5 11.20 12.57 0.18 232 2.24
1.9 6.72 11.17 0.23 232 2.24
1.9 8.11 11.17 0.23 232 2.24

Model confidence intervals

bind_cols(my_mpg |> select(displ, city_l100km),
          predict(m1, interval = "confidence") |> as_tibble() ) |>
  distinct() |> kable(digits = 2)
displ city_l100km fit lwr upr
1.8 13.07 10.93 10.46 11.40
1.8 11.20 10.93 10.46 11.40
2.0 11.76 11.40 10.96 11.84
2.0 11.20 11.40 10.96 11.84
2.8 14.70 13.27 12.95 13.60
2.8 13.07 13.27 12.95 13.60
3.1 13.07 13.97 13.67 14.27
1.8 14.70 10.93 10.46 11.40
2.0 12.38 11.40 10.96 11.84
2.8 15.68 13.27 12.95 13.60
2.8 13.84 13.27 12.95 13.60
3.1 13.84 13.97 13.67 14.27
3.1 15.68 13.97 13.67 14.27
4.2 14.70 16.54 16.21 16.88
5.3 16.80 19.12 18.62 19.62
5.3 21.38 19.12 18.62 19.62
5.7 18.09 20.05 19.48 20.63
6.0 19.60 20.75 20.12 21.39
5.7 14.70 20.05 19.48 20.63
5.7 15.68 20.05 19.48 20.63
6.2 14.70 21.22 20.55 21.90
6.2 15.68 21.22 20.55 21.90
7.0 15.68 23.09 22.25 23.93
5.7 21.38 20.05 19.48 20.63
6.5 16.80 21.92 21.19 22.66
2.4 12.38 12.34 11.96 12.71
2.4 10.69 12.34 11.96 12.71
3.5 13.07 14.91 14.62 15.20
3.6 13.84 15.14 14.85 15.43
2.4 13.07 12.34 11.96 12.71
3.0 13.84 13.74 13.43 14.05
3.3 14.70 14.44 14.15 14.73
3.3 13.84 14.44 14.15 14.73
3.3 21.38 14.44 14.15 14.73
3.8 15.68 15.61 15.31 15.91
3.8 14.70 15.61 15.31 15.91
4.0 14.70 16.08 15.76 16.39
3.7 15.68 15.37 15.08 15.67
3.7 16.80 15.37 15.08 15.67
3.9 18.09 15.84 15.54 16.15
3.9 16.80 15.84 15.54 16.15
4.7 16.80 17.71 17.31 18.11
4.7 26.13 17.71 17.31 18.11
5.2 21.38 18.88 18.40 19.36
4.7 18.09 17.71 17.31 18.11
5.9 21.38 20.52 19.90 21.13
4.7 19.60 17.71 17.31 18.11
4.6 21.38 17.48 17.10 17.86
5.4 21.38 19.35 18.83 19.87
5.4 19.60 19.35 18.83 19.87
4.0 16.80 16.08 15.76 16.39
4.0 15.68 16.08 15.76 16.39
4.0 18.09 16.08 15.76 16.39
4.6 18.09 17.48 17.10 17.86
5.0 18.09 18.41 17.97 18.86
4.2 16.80 16.54 16.21 16.88
5.4 18.09 19.35 18.83 19.87
3.8 13.07 15.61 15.31 15.91
4.0 13.84 16.08 15.76 16.39
4.6 15.68 17.48 17.10 17.86
5.4 16.80 19.35 18.83 19.87
1.6 8.40 10.46 9.96 10.97
1.6 9.80 10.46 9.96 10.97
1.6 9.41 10.46 9.96 10.97
1.6 10.23 10.46 9.96 10.97
1.8 9.05 10.93 10.46 11.40
1.8 9.41 10.93 10.46 11.40
1.8 9.80 10.93 10.46 11.40
2.4 11.20 12.34 11.96 12.71
2.5 13.07 12.57 12.21 12.93
3.3 12.38 14.44 14.15 14.73
2.7 13.84 13.04 12.70 13.37
2.7 14.70 13.04 12.70 13.37
6.1 21.38 20.99 20.33 21.64
4.0 21.38 16.08 15.76 16.39
4.2 19.60 16.54 16.21 16.88
4.4 19.60 17.01 16.66 17.37
2.5 10.23 12.57 12.21 12.93
3.5 12.38 14.91 14.62 15.20
3.0 13.07 13.74 13.43 14.05
3.0 12.38 13.74 13.43 14.05
3.3 16.80 14.44 14.15 14.73
3.3 15.68 14.44 14.15 14.73
5.6 19.60 19.82 19.26 20.37
3.8 13.84 15.61 15.31 15.91
5.3 14.70 19.12 18.62 19.62
2.5 11.76 12.57 12.21 12.93
2.5 12.38 12.57 12.21 12.93
2.2 11.20 11.87 11.46 12.27
2.2 12.38 11.87 11.46 12.27
2.7 15.68 13.04 12.70 13.37
3.4 15.68 14.67 14.38 14.96
3.3 13.07 14.44 14.15 14.73
1.8 8.40 10.93 10.46 11.40
4.7 21.38 17.71 17.31 18.11
2.0 10.69 11.40 10.96 11.84
1.9 7.13 11.17 10.71 11.62
2.5 11.20 12.57 12.21 12.93
1.9 6.72 11.17 10.71 11.62
1.9 8.11 11.17 10.71 11.62

Prediction uncertainties

bind_cols(new_data,
          predict(m1, new_data, interval = "prediction") |> 
            as_tibble() ) |> kable(digits = 2)
displ fit lwr upr
1.6 10.46 6.02 14.90
2.1 11.63 7.20 16.06
2.6 12.80 8.38 17.23
3.1 13.97 9.55 18.39
3.6 15.14 10.72 19.56
4.1 16.31 11.89 20.73
4.6 17.48 13.05 21.91
5.1 18.65 14.21 23.08
5.6 19.82 15.37 24.26
6.1 20.99 16.53 25.45
6.6 22.16 17.68 26.63
7.1 23.33 18.83 27.82

Easier: augment

augment(m1, my_mpg, interval = "confidence") |>
  select(displ, city_l100km, .fitted, .lower, .upper, .resid, everything() ) |> kable(digits = 2)
displ city_l100km .fitted .lower .upper .resid manufacturer model year cyl trans drv cty hwy fl class .hat .sigma .cooksd .std.resid
1.8 13.07 10.93 10.46 11.40 2.14 audi a4 1999 4 auto(l5) f 18 29 p compact 0.01 2.24 0.01 0.96
1.8 11.20 10.93 10.46 11.40 0.27 audi a4 1999 4 manual(m5) f 21 29 p compact 0.01 2.24 0.00 0.12
2.0 11.76 11.40 10.96 11.84 0.36 audi a4 2008 4 manual(m6) f 20 31 p compact 0.01 2.24 0.00 0.16
2.0 11.20 11.40 10.96 11.84 -0.20 audi a4 2008 4 auto(av) f 21 30 p compact 0.01 2.24 0.00 -0.09
2.8 14.70 13.27 12.95 13.60 1.43 audi a4 1999 6 auto(l5) f 16 26 p compact 0.01 2.24 0.00 0.64
2.8 13.07 13.27 12.95 13.60 -0.20 audi a4 1999 6 manual(m5) f 18 26 p compact 0.01 2.24 0.00 -0.09
3.1 13.07 13.97 13.67 14.27 -0.90 audi a4 2008 6 auto(av) f 18 27 p compact 0.00 2.24 0.00 -0.40
1.8 13.07 10.93 10.46 11.40 2.14 audi a4 quattro 1999 4 manual(m5) 4 18 26 p compact 0.01 2.24 0.01 0.96
1.8 14.70 10.93 10.46 11.40 3.77 audi a4 quattro 1999 4 auto(l5) 4 16 25 p compact 0.01 2.23 0.02 1.69
2.0 11.76 11.40 10.96 11.84 0.36 audi a4 quattro 2008 4 manual(m6) 4 20 28 p compact 0.01 2.24 0.00 0.16
2.0 12.38 11.40 10.96 11.84 0.98 audi a4 quattro 2008 4 auto(s6) 4 19 27 p compact 0.01 2.24 0.00 0.44
2.8 15.68 13.27 12.95 13.60 2.41 audi a4 quattro 1999 6 auto(l5) 4 15 25 p compact 0.01 2.24 0.00 1.08
2.8 13.84 13.27 12.95 13.60 0.57 audi a4 quattro 1999 6 manual(m5) 4 17 25 p compact 0.01 2.24 0.00 0.25
3.1 13.84 13.97 13.67 14.27 -0.14 audi a4 quattro 2008 6 auto(s6) 4 17 25 p compact 0.00 2.24 0.00 -0.06
3.1 15.68 13.97 13.67 14.27 1.71 audi a4 quattro 2008 6 manual(m6) 4 15 25 p compact 0.00 2.24 0.00 0.77
2.8 15.68 13.27 12.95 13.60 2.41 audi a6 quattro 1999 6 auto(l5) 4 15 24 p midsize 0.01 2.24 0.00 1.08
3.1 13.84 13.97 13.67 14.27 -0.14 audi a6 quattro 2008 6 auto(s6) 4 17 25 p midsize 0.00 2.24 0.00 -0.06
4.2 14.70 16.54 16.21 16.88 -1.84 audi a6 quattro 2008 8 auto(s6) 4 16 23 p midsize 0.01 2.24 0.00 -0.83
5.3 16.80 19.12 18.62 19.62 -2.32 chevrolet c1500 suburban 2wd 2008 8 auto(l4) r 14 20 r suv 0.01 2.24 0.01 -1.04
5.3 21.38 19.12 18.62 19.62 2.27 chevrolet c1500 suburban 2wd 2008 8 auto(l4) r 11 15 e suv 0.01 2.24 0.01 1.02
5.3 16.80 19.12 18.62 19.62 -2.32 chevrolet c1500 suburban 2wd 2008 8 auto(l4) r 14 20 r suv 0.01 2.24 0.01 -1.04
5.7 18.09 20.05 19.48 20.63 -1.96 chevrolet c1500 suburban 2wd 1999 8 auto(l4) r 13 17 r suv 0.02 2.24 0.01 -0.88
6.0 19.60 20.75 20.12 21.39 -1.15 chevrolet c1500 suburban 2wd 2008 8 auto(l4) r 12 17 r suv 0.02 2.24 0.00 -0.52
5.7 14.70 20.05 19.48 20.63 -5.35 chevrolet corvette 1999 8 manual(m6) r 16 26 p 2seater 0.02 2.22 0.05 -2.41
5.7 15.68 20.05 19.48 20.63 -4.37 chevrolet corvette 1999 8 auto(l4) r 15 23 p 2seater 0.02 2.22 0.03 -1.97
6.2 14.70 21.22 20.55 21.90 -6.52 chevrolet corvette 2008 8 manual(m6) r 16 26 p 2seater 0.02 2.20 0.10 -2.95
6.2 15.68 21.22 20.55 21.90 -5.54 chevrolet corvette 2008 8 auto(s6) r 15 25 p 2seater 0.02 2.21 0.08 -2.50
7.0 15.68 23.09 22.25 23.93 -7.41 chevrolet corvette 2008 8 manual(m6) r 15 24 p 2seater 0.04 2.19 0.21 -3.37
5.3 16.80 19.12 18.62 19.62 -2.32 chevrolet k1500 tahoe 4wd 2008 8 auto(l4) 4 14 19 r suv 0.01 2.24 0.01 -1.04
5.3 21.38 19.12 18.62 19.62 2.27 chevrolet k1500 tahoe 4wd 2008 8 auto(l4) 4 11 14 e suv 0.01 2.24 0.01 1.02
5.7 21.38 20.05 19.48 20.63 1.33 chevrolet k1500 tahoe 4wd 1999 8 auto(l4) 4 11 15 r suv 0.02 2.24 0.00 0.60
6.5 16.80 21.92 21.19 22.66 -5.12 chevrolet k1500 tahoe 4wd 1999 8 auto(l4) 4 14 17 d suv 0.03 2.22 0.08 -2.32
2.4 12.38 12.34 11.96 12.71 0.04 chevrolet malibu 1999 4 auto(l4) f 19 27 r midsize 0.01 2.24 0.00 0.02
2.4 10.69 12.34 11.96 12.71 -1.64 chevrolet malibu 2008 4 auto(l4) f 22 30 r midsize 0.01 2.24 0.00 -0.74
3.1 13.07 13.97 13.67 14.27 -0.90 chevrolet malibu 1999 6 auto(l4) f 18 26 r midsize 0.00 2.24 0.00 -0.40
3.5 13.07 14.91 14.62 15.20 -1.84 chevrolet malibu 2008 6 auto(l4) f 18 29 r midsize 0.00 2.24 0.00 -0.82
3.6 13.84 15.14 14.85 15.43 -1.30 chevrolet malibu 2008 6 auto(s6) f 17 26 r midsize 0.00 2.24 0.00 -0.58
2.4 13.07 12.34 11.96 12.71 0.73 dodge caravan 2wd 1999 4 auto(l3) f 18 24 r minivan 0.01 2.24 0.00 0.33
3.0 13.84 13.74 13.43 14.05 0.10 dodge caravan 2wd 1999 6 auto(l4) f 17 24 r minivan 0.00 2.24 0.00 0.04
3.3 14.70 14.44 14.15 14.73 0.26 dodge caravan 2wd 1999 6 auto(l4) f 16 22 r minivan 0.00 2.24 0.00 0.12
3.3 14.70 14.44 14.15 14.73 0.26 dodge caravan 2wd 1999 6 auto(l4) f 16 22 r minivan 0.00 2.24 0.00 0.12
3.3 13.84 14.44 14.15 14.73 -0.60 dodge caravan 2wd 2008 6 auto(l4) f 17 24 r minivan 0.00 2.24 0.00 -0.27
3.3 13.84 14.44 14.15 14.73 -0.60 dodge caravan 2wd 2008 6 auto(l4) f 17 24 r minivan 0.00 2.24 0.00 -0.27
3.3 21.38 14.44 14.15 14.73 6.94 dodge caravan 2wd 2008 6 auto(l4) f 11 17 e minivan 0.00 2.20 0.02 3.11
3.8 15.68 15.61 15.31 15.91 0.07 dodge caravan 2wd 1999 6 auto(l4) f 15 22 r minivan 0.00 2.24 0.00 0.03
3.8 15.68 15.61 15.31 15.91 0.07 dodge caravan 2wd 1999 6 auto(l4) f 15 21 r minivan 0.00 2.24 0.00 0.03
3.8 14.70 15.61 15.31 15.91 -0.91 dodge caravan 2wd 2008 6 auto(l6) f 16 23 r minivan 0.00 2.24 0.00 -0.41
4.0 14.70 16.08 15.76 16.39 -1.38 dodge caravan 2wd 2008 6 auto(l6) f 16 23 r minivan 0.00 2.24 0.00 -0.62
3.7 15.68 15.37 15.08 15.67 0.31 dodge dakota pickup 4wd 2008 6 manual(m6) 4 15 19 r pickup 0.00 2.24 0.00 0.14
3.7 16.80 15.37 15.08 15.67 1.43 dodge dakota pickup 4wd 2008 6 auto(l4) 4 14 18 r pickup 0.00 2.24 0.00 0.64
3.9 18.09 15.84 15.54 16.15 2.25 dodge dakota pickup 4wd 1999 6 auto(l4) 4 13 17 r pickup 0.00 2.24 0.00 1.01
3.9 16.80 15.84 15.54 16.15 0.96 dodge dakota pickup 4wd 1999 6 manual(m5) 4 14 17 r pickup 0.00 2.24 0.00 0.43
4.7 16.80 17.71 17.31 18.11 -0.91 dodge dakota pickup 4wd 2008 8 auto(l5) 4 14 19 r pickup 0.01 2.24 0.00 -0.41
4.7 16.80 17.71 17.31 18.11 -0.91 dodge dakota pickup 4wd 2008 8 auto(l5) 4 14 19 r pickup 0.01 2.24 0.00 -0.41
4.7 26.13 17.71 17.31 18.11 8.42 dodge dakota pickup 4wd 2008 8 auto(l5) 4 9 12 e pickup 0.01 2.17 0.06 3.78
5.2 21.38 18.88 18.40 19.36 2.50 dodge dakota pickup 4wd 1999 8 manual(m5) 4 11 17 r pickup 0.01 2.24 0.01 1.12
5.2 21.38 18.88 18.40 19.36 2.50 dodge dakota pickup 4wd 1999 8 auto(l4) 4 11 15 r pickup 0.01 2.24 0.01 1.12
3.9 18.09 15.84 15.54 16.15 2.25 dodge durango 4wd 1999 6 auto(l4) 4 13 17 r suv 0.00 2.24 0.00 1.01
4.7 18.09 17.71 17.31 18.11 0.38 dodge durango 4wd 2008 8 auto(l5) 4 13 17 r suv 0.01 2.24 0.00 0.17
4.7 26.13 17.71 17.31 18.11 8.42 dodge durango 4wd 2008 8 auto(l5) 4 9 12 e suv 0.01 2.17 0.06 3.78
4.7 18.09 17.71 17.31 18.11 0.38 dodge durango 4wd 2008 8 auto(l5) 4 13 17 r suv 0.01 2.24 0.00 0.17
5.2 21.38 18.88 18.40 19.36 2.50 dodge durango 4wd 1999 8 auto(l4) 4 11 16 r suv 0.01 2.24 0.01 1.12
5.7 18.09 20.05 19.48 20.63 -1.96 dodge durango 4wd 2008 8 auto(l5) 4 13 18 r suv 0.02 2.24 0.01 -0.88
5.9 21.38 20.52 19.90 21.13 0.86 dodge durango 4wd 1999 8 auto(l4) 4 11 15 r suv 0.02 2.24 0.00 0.39
4.7 19.60 17.71 17.31 18.11 1.89 dodge ram 1500 pickup 4wd 2008 8 manual(m6) 4 12 16 r pickup 0.01 2.24 0.00 0.85
4.7 26.13 17.71 17.31 18.11 8.42 dodge ram 1500 pickup 4wd 2008 8 auto(l5) 4 9 12 e pickup 0.01 2.17 0.06 3.78
4.7 18.09 17.71 17.31 18.11 0.38 dodge ram 1500 pickup 4wd 2008 8 auto(l5) 4 13 17 r pickup 0.01 2.24 0.00 0.17
4.7 18.09 17.71 17.31 18.11 0.38 dodge ram 1500 pickup 4wd 2008 8 auto(l5) 4 13 17 r pickup 0.01 2.24 0.00 0.17
4.7 19.60 17.71 17.31 18.11 1.89 dodge ram 1500 pickup 4wd 2008 8 manual(m6) 4 12 16 r pickup 0.01 2.24 0.00 0.85
4.7 26.13 17.71 17.31 18.11 8.42 dodge ram 1500 pickup 4wd 2008 8 manual(m6) 4 9 12 e pickup 0.01 2.17 0.06 3.78
5.2 21.38 18.88 18.40 19.36 2.50 dodge ram 1500 pickup 4wd 1999 8 auto(l4) 4 11 15 r pickup 0.01 2.24 0.01 1.12
5.2 21.38 18.88 18.40 19.36 2.50 dodge ram 1500 pickup 4wd 1999 8 manual(m5) 4 11 16 r pickup 0.01 2.24 0.01 1.12
5.7 18.09 20.05 19.48 20.63 -1.96 dodge ram 1500 pickup 4wd 2008 8 auto(l5) 4 13 17 r pickup 0.02 2.24 0.01 -0.88
5.9 21.38 20.52 19.90 21.13 0.86 dodge ram 1500 pickup 4wd 1999 8 auto(l4) 4 11 15 r pickup 0.02 2.24 0.00 0.39
4.6 21.38 17.48 17.10 17.86 3.90 ford expedition 2wd 1999 8 auto(l4) r 11 17 r suv 0.01 2.23 0.01 1.75
5.4 21.38 19.35 18.83 19.87 2.03 ford expedition 2wd 1999 8 auto(l4) r 11 17 r suv 0.01 2.24 0.01 0.91
5.4 19.60 19.35 18.83 19.87 0.25 ford expedition 2wd 2008 8 auto(l6) r 12 18 r suv 0.01 2.24 0.00 0.11
4.0 16.80 16.08 15.76 16.39 0.72 ford explorer 4wd 1999 6 auto(l5) 4 14 17 r suv 0.00 2.24 0.00 0.32
4.0 15.68 16.08 15.76 16.39 -0.40 ford explorer 4wd 1999 6 manual(m5) 4 15 19 r suv 0.00 2.24 0.00 -0.18
4.0 16.80 16.08 15.76 16.39 0.72 ford explorer 4wd 1999 6 auto(l5) 4 14 17 r suv 0.00 2.24 0.00 0.32
4.0 18.09 16.08 15.76 16.39 2.02 ford explorer 4wd 2008 6 auto(l5) 4 13 19 r suv 0.00 2.24 0.00 0.90
4.6 18.09 17.48 17.10 17.86 0.61 ford explorer 4wd 2008 8 auto(l6) 4 13 19 r suv 0.01 2.24 0.00 0.28
5.0 18.09 18.41 17.97 18.86 -0.32 ford explorer 4wd 1999 8 auto(l4) 4 13 17 r suv 0.01 2.24 0.00 -0.14
4.2 16.80 16.54 16.21 16.88 0.26 ford f150 pickup 4wd 1999 6 auto(l4) 4 14 17 r pickup 0.01 2.24 0.00 0.12
4.2 16.80 16.54 16.21 16.88 0.26 ford f150 pickup 4wd 1999 6 manual(m5) 4 14 17 r pickup 0.01 2.24 0.00 0.12
4.6 18.09 17.48 17.10 17.86 0.61 ford f150 pickup 4wd 1999 8 manual(m5) 4 13 16 r pickup 0.01 2.24 0.00 0.28
4.6 18.09 17.48 17.10 17.86 0.61 ford f150 pickup 4wd 1999 8 auto(l4) 4 13 16 r pickup 0.01 2.24 0.00 0.28
4.6 18.09 17.48 17.10 17.86 0.61 ford f150 pickup 4wd 2008 8 auto(l4) 4 13 17 r pickup 0.01 2.24 0.00 0.28
5.4 21.38 19.35 18.83 19.87 2.03 ford f150 pickup 4wd 1999 8 auto(l4) 4 11 15 r pickup 0.01 2.24 0.01 0.91
5.4 18.09 19.35 18.83 19.87 -1.26 ford f150 pickup 4wd 2008 8 auto(l4) 4 13 17 r pickup 0.01 2.24 0.00 -0.57
3.8 13.07 15.61 15.31 15.91 -2.54 ford mustang 1999 6 manual(m5) r 18 26 r subcompact 0.00 2.24 0.00 -1.14
3.8 13.07 15.61 15.31 15.91 -2.54 ford mustang 1999 6 auto(l4) r 18 25 r subcompact 0.00 2.24 0.00 -1.14
4.0 13.84 16.08 15.76 16.39 -2.24 ford mustang 2008 6 manual(m5) r 17 26 r subcompact 0.00 2.24 0.00 -1.00
4.0 14.70 16.08 15.76 16.39 -1.38 ford mustang 2008 6 auto(l5) r 16 24 r subcompact 0.00 2.24 0.00 -0.62
4.6 15.68 17.48 17.10 17.86 -1.80 ford mustang 1999 8 auto(l4) r 15 21 r subcompact 0.01 2.24 0.00 -0.81
4.6 15.68 17.48 17.10 17.86 -1.80 ford mustang 1999 8 manual(m5) r 15 22 r subcompact 0.01 2.24 0.00 -0.81
4.6 15.68 17.48 17.10 17.86 -1.80 ford mustang 2008 8 manual(m5) r 15 23 r subcompact 0.01 2.24 0.00 -0.81
4.6 15.68 17.48 17.10 17.86 -1.80 ford mustang 2008 8 auto(l5) r 15 22 r subcompact 0.01 2.24 0.00 -0.81
5.4 16.80 19.35 18.83 19.87 -2.55 ford mustang 2008 8 manual(m6) r 14 20 p subcompact 0.01 2.24 0.01 -1.15
1.6 8.40 10.46 9.96 10.97 -2.06 honda civic 1999 4 manual(m5) f 28 33 r subcompact 0.01 2.24 0.01 -0.93
1.6 9.80 10.46 9.96 10.97 -0.66 honda civic 1999 4 auto(l4) f 24 32 r subcompact 0.01 2.24 0.00 -0.30
1.6 9.41 10.46 9.96 10.97 -1.06 honda civic 1999 4 manual(m5) f 25 32 r subcompact 0.01 2.24 0.00 -0.47
1.6 10.23 10.46 9.96 10.97 -0.24 honda civic 1999 4 manual(m5) f 23 29 p subcompact 0.01 2.24 0.00 -0.11
1.6 9.80 10.46 9.96 10.97 -0.66 honda civic 1999 4 auto(l4) f 24 32 r subcompact 0.01 2.24 0.00 -0.30
1.8 9.05 10.93 10.46 11.40 -1.89 honda civic 2008 4 manual(m5) f 26 34 r subcompact 0.01 2.24 0.00 -0.85
1.8 9.41 10.93 10.46 11.40 -1.52 honda civic 2008 4 auto(l5) f 25 36 r subcompact 0.01 2.24 0.00 -0.68
1.8 9.80 10.93 10.46 11.40 -1.13 honda civic 2008 4 auto(l5) f 24 36 c subcompact 0.01 2.24 0.00 -0.51
2.0 11.20 11.40 10.96 11.84 -0.20 honda civic 2008 4 manual(m6) f 21 29 p subcompact 0.01 2.24 0.00 -0.09
2.4 13.07 12.34 11.96 12.71 0.73 hyundai sonata 1999 4 auto(l4) f 18 26 r midsize 0.01 2.24 0.00 0.33
2.4 13.07 12.34 11.96 12.71 0.73 hyundai sonata 1999 4 manual(m5) f 18 27 r midsize 0.01 2.24 0.00 0.33
2.4 11.20 12.34 11.96 12.71 -1.13 hyundai sonata 2008 4 auto(l4) f 21 30 r midsize 0.01 2.24 0.00 -0.51
2.4 11.20 12.34 11.96 12.71 -1.13 hyundai sonata 2008 4 manual(m5) f 21 31 r midsize 0.01 2.24 0.00 -0.51
2.5 13.07 12.57 12.21 12.93 0.50 hyundai sonata 1999 6 auto(l4) f 18 26 r midsize 0.01 2.24 0.00 0.22
2.5 13.07 12.57 12.21 12.93 0.50 hyundai sonata 1999 6 manual(m5) f 18 26 r midsize 0.01 2.24 0.00 0.22
3.3 12.38 14.44 14.15 14.73 -2.06 hyundai sonata 2008 6 auto(l5) f 19 28 r midsize 0.00 2.24 0.00 -0.92
2.0 12.38 11.40 10.96 11.84 0.98 hyundai tiburon 1999 4 auto(l4) f 19 26 r subcompact 0.01 2.24 0.00 0.44
2.0 12.38 11.40 10.96 11.84 0.98 hyundai tiburon 1999 4 manual(m5) f 19 29 r subcompact 0.01 2.24 0.00 0.44
2.0 11.76 11.40 10.96 11.84 0.36 hyundai tiburon 2008 4 manual(m5) f 20 28 r subcompact 0.01 2.24 0.00 0.16
2.0 11.76 11.40 10.96 11.84 0.36 hyundai tiburon 2008 4 auto(l4) f 20 27 r subcompact 0.01 2.24 0.00 0.16
2.7 13.84 13.04 12.70 13.37 0.80 hyundai tiburon 2008 6 auto(l4) f 17 24 r subcompact 0.01 2.24 0.00 0.36
2.7 14.70 13.04 12.70 13.37 1.66 hyundai tiburon 2008 6 manual(m6) f 16 24 r subcompact 0.01 2.24 0.00 0.75
2.7 13.84 13.04 12.70 13.37 0.80 hyundai tiburon 2008 6 manual(m5) f 17 24 r subcompact 0.01 2.24 0.00 0.36
3.0 13.84 13.74 13.43 14.05 0.10 jeep grand cherokee 4wd 2008 6 auto(l5) 4 17 22 d suv 0.00 2.24 0.00 0.04
3.7 15.68 15.37 15.08 15.67 0.31 jeep grand cherokee 4wd 2008 6 auto(l5) 4 15 19 r suv 0.00 2.24 0.00 0.14
4.0 15.68 16.08 15.76 16.39 -0.40 jeep grand cherokee 4wd 1999 6 auto(l4) 4 15 20 r suv 0.00 2.24 0.00 -0.18
4.7 16.80 17.71 17.31 18.11 -0.91 jeep grand cherokee 4wd 1999 8 auto(l4) 4 14 17 r suv 0.01 2.24 0.00 -0.41
4.7 26.13 17.71 17.31 18.11 8.42 jeep grand cherokee 4wd 2008 8 auto(l5) 4 9 12 e suv 0.01 2.17 0.06 3.78
4.7 16.80 17.71 17.31 18.11 -0.91 jeep grand cherokee 4wd 2008 8 auto(l5) 4 14 19 r suv 0.01 2.24 0.00 -0.41
5.7 18.09 20.05 19.48 20.63 -1.96 jeep grand cherokee 4wd 2008 8 auto(l5) 4 13 18 r suv 0.02 2.24 0.01 -0.88
6.1 21.38 20.99 20.33 21.64 0.40 jeep grand cherokee 4wd 2008 8 auto(l5) 4 11 14 p suv 0.02 2.24 0.00 0.18
4.0 21.38 16.08 15.76 16.39 5.31 land rover range rover 1999 8 auto(l4) 4 11 15 p suv 0.00 2.22 0.01 2.38
4.2 19.60 16.54 16.21 16.88 3.06 land rover range rover 2008 8 auto(s6) 4 12 18 r suv 0.01 2.23 0.01 1.37
4.4 19.60 17.01 16.66 17.37 2.59 land rover range rover 2008 8 auto(s6) 4 12 18 r suv 0.01 2.24 0.00 1.16
4.6 21.38 17.48 17.10 17.86 3.90 land rover range rover 1999 8 auto(l4) 4 11 15 p suv 0.01 2.23 0.01 1.75
5.4 21.38 19.35 18.83 19.87 2.03 lincoln navigator 2wd 1999 8 auto(l4) r 11 17 r suv 0.01 2.24 0.01 0.91
5.4 21.38 19.35 18.83 19.87 2.03 lincoln navigator 2wd 1999 8 auto(l4) r 11 16 p suv 0.01 2.24 0.01 0.91
5.4 19.60 19.35 18.83 19.87 0.25 lincoln navigator 2wd 2008 8 auto(l6) r 12 18 r suv 0.01 2.24 0.00 0.11
4.0 16.80 16.08 15.76 16.39 0.72 mercury mountaineer 4wd 1999 6 auto(l5) 4 14 17 r suv 0.00 2.24 0.00 0.32
4.0 18.09 16.08 15.76 16.39 2.02 mercury mountaineer 4wd 2008 6 auto(l5) 4 13 19 r suv 0.00 2.24 0.00 0.90
4.6 18.09 17.48 17.10 17.86 0.61 mercury mountaineer 4wd 2008 8 auto(l6) 4 13 19 r suv 0.01 2.24 0.00 0.28
5.0 18.09 18.41 17.97 18.86 -0.32 mercury mountaineer 4wd 1999 8 auto(l4) 4 13 17 r suv 0.01 2.24 0.00 -0.14
2.4 11.20 12.34 11.96 12.71 -1.13 nissan altima 1999 4 manual(m5) f 21 29 r compact 0.01 2.24 0.00 -0.51
2.4 12.38 12.34 11.96 12.71 0.04 nissan altima 1999 4 auto(l4) f 19 27 r compact 0.01 2.24 0.00 0.02
2.5 10.23 12.57 12.21 12.93 -2.34 nissan altima 2008 4 auto(av) f 23 31 r midsize 0.01 2.24 0.00 -1.05
2.5 10.23 12.57 12.21 12.93 -2.34 nissan altima 2008 4 manual(m6) f 23 32 r midsize 0.01 2.24 0.00 -1.05
3.5 12.38 14.91 14.62 15.20 -2.53 nissan altima 2008 6 manual(m6) f 19 27 p midsize 0.00 2.24 0.00 -1.13
3.5 12.38 14.91 14.62 15.20 -2.53 nissan altima 2008 6 auto(av) f 19 26 p midsize 0.00 2.24 0.00 -1.13
3.0 13.07 13.74 13.43 14.05 -0.67 nissan maxima 1999 6 auto(l4) f 18 26 r midsize 0.00 2.24 0.00 -0.30
3.0 12.38 13.74 13.43 14.05 -1.36 nissan maxima 1999 6 manual(m5) f 19 25 r midsize 0.00 2.24 0.00 -0.61
3.5 12.38 14.91 14.62 15.20 -2.53 nissan maxima 2008 6 auto(av) f 19 25 p midsize 0.00 2.24 0.00 -1.13
3.3 16.80 14.44 14.15 14.73 2.36 nissan pathfinder 4wd 1999 6 auto(l4) 4 14 17 r suv 0.00 2.24 0.00 1.06
3.3 15.68 14.44 14.15 14.73 1.24 nissan pathfinder 4wd 1999 6 manual(m5) 4 15 17 r suv 0.00 2.24 0.00 0.56
4.0 16.80 16.08 15.76 16.39 0.72 nissan pathfinder 4wd 2008 6 auto(l5) 4 14 20 p suv 0.00 2.24 0.00 0.32
5.6 19.60 19.82 19.26 20.37 -0.22 nissan pathfinder 4wd 2008 8 auto(s5) 4 12 18 p suv 0.02 2.24 0.00 -0.10
3.1 13.07 13.97 13.67 14.27 -0.90 pontiac grand prix 1999 6 auto(l4) f 18 26 r midsize 0.00 2.24 0.00 -0.40
3.8 14.70 15.61 15.31 15.91 -0.91 pontiac grand prix 1999 6 auto(l4) f 16 26 p midsize 0.00 2.24 0.00 -0.41
3.8 13.84 15.61 15.31 15.91 -1.77 pontiac grand prix 1999 6 auto(l4) f 17 27 r midsize 0.00 2.24 0.00 -0.79
3.8 13.07 15.61 15.31 15.91 -2.54 pontiac grand prix 2008 6 auto(l4) f 18 28 r midsize 0.00 2.24 0.00 -1.14
5.3 14.70 19.12 18.62 19.62 -4.42 pontiac grand prix 2008 8 auto(s4) f 16 25 p midsize 0.01 2.22 0.03 -1.99
2.5 13.07 12.57 12.21 12.93 0.50 subaru forester awd 1999 4 manual(m5) 4 18 25 r suv 0.01 2.24 0.00 0.22
2.5 13.07 12.57 12.21 12.93 0.50 subaru forester awd 1999 4 auto(l4) 4 18 24 r suv 0.01 2.24 0.00 0.22
2.5 11.76 12.57 12.21 12.93 -0.81 subaru forester awd 2008 4 manual(m5) 4 20 27 r suv 0.01 2.24 0.00 -0.36
2.5 12.38 12.57 12.21 12.93 -0.19 subaru forester awd 2008 4 manual(m5) 4 19 25 p suv 0.01 2.24 0.00 -0.08
2.5 11.76 12.57 12.21 12.93 -0.81 subaru forester awd 2008 4 auto(l4) 4 20 26 r suv 0.01 2.24 0.00 -0.36
2.5 13.07 12.57 12.21 12.93 0.50 subaru forester awd 2008 4 auto(l4) 4 18 23 p suv 0.01 2.24 0.00 0.22
2.2 11.20 11.87 11.46 12.27 -0.67 subaru impreza awd 1999 4 auto(l4) 4 21 26 r subcompact 0.01 2.24 0.00 -0.30
2.2 12.38 11.87 11.46 12.27 0.51 subaru impreza awd 1999 4 manual(m5) 4 19 26 r subcompact 0.01 2.24 0.00 0.23
2.5 12.38 12.57 12.21 12.93 -0.19 subaru impreza awd 1999 4 manual(m5) 4 19 26 r subcompact 0.01 2.24 0.00 -0.08
2.5 12.38 12.57 12.21 12.93 -0.19 subaru impreza awd 1999 4 auto(l4) 4 19 26 r subcompact 0.01 2.24 0.00 -0.08
2.5 11.76 12.57 12.21 12.93 -0.81 subaru impreza awd 2008 4 auto(s4) 4 20 25 p compact 0.01 2.24 0.00 -0.36
2.5 11.76 12.57 12.21 12.93 -0.81 subaru impreza awd 2008 4 auto(s4) 4 20 27 r compact 0.01 2.24 0.00 -0.36
2.5 12.38 12.57 12.21 12.93 -0.19 subaru impreza awd 2008 4 manual(m5) 4 19 25 p compact 0.01 2.24 0.00 -0.08
2.5 11.76 12.57 12.21 12.93 -0.81 subaru impreza awd 2008 4 manual(m5) 4 20 27 r compact 0.01 2.24 0.00 -0.36
2.7 15.68 13.04 12.70 13.37 2.64 toyota 4runner 4wd 1999 4 manual(m5) 4 15 20 r suv 0.01 2.24 0.00 1.18
2.7 14.70 13.04 12.70 13.37 1.66 toyota 4runner 4wd 1999 4 auto(l4) 4 16 20 r suv 0.01 2.24 0.00 0.75
3.4 15.68 14.67 14.38 14.96 1.01 toyota 4runner 4wd 1999 6 auto(l4) 4 15 19 r suv 0.00 2.24 0.00 0.45
3.4 15.68 14.67 14.38 14.96 1.01 toyota 4runner 4wd 1999 6 manual(m5) 4 15 17 r suv 0.00 2.24 0.00 0.45
4.0 14.70 16.08 15.76 16.39 -1.38 toyota 4runner 4wd 2008 6 auto(l5) 4 16 20 r suv 0.00 2.24 0.00 -0.62
4.7 16.80 17.71 17.31 18.11 -0.91 toyota 4runner 4wd 2008 8 auto(l5) 4 14 17 r suv 0.01 2.24 0.00 -0.41
2.2 11.20 11.87 11.46 12.27 -0.67 toyota camry 1999 4 manual(m5) f 21 29 r midsize 0.01 2.24 0.00 -0.30
2.2 11.20 11.87 11.46 12.27 -0.67 toyota camry 1999 4 auto(l4) f 21 27 r midsize 0.01 2.24 0.00 -0.30
2.4 11.20 12.34 11.96 12.71 -1.13 toyota camry 2008 4 manual(m5) f 21 31 r midsize 0.01 2.24 0.00 -0.51
2.4 11.20 12.34 11.96 12.71 -1.13 toyota camry 2008 4 auto(l5) f 21 31 r midsize 0.01 2.24 0.00 -0.51
3.0 13.07 13.74 13.43 14.05 -0.67 toyota camry 1999 6 auto(l4) f 18 26 r midsize 0.00 2.24 0.00 -0.30
3.0 13.07 13.74 13.43 14.05 -0.67 toyota camry 1999 6 manual(m5) f 18 26 r midsize 0.00 2.24 0.00 -0.30
3.5 12.38 14.91 14.62 15.20 -2.53 toyota camry 2008 6 auto(s6) f 19 28 r midsize 0.00 2.24 0.00 -1.13
2.2 11.20 11.87 11.46 12.27 -0.67 toyota camry solara 1999 4 auto(l4) f 21 27 r compact 0.01 2.24 0.00 -0.30
2.2 11.20 11.87 11.46 12.27 -0.67 toyota camry solara 1999 4 manual(m5) f 21 29 r compact 0.01 2.24 0.00 -0.30
2.4 11.20 12.34 11.96 12.71 -1.13 toyota camry solara 2008 4 manual(m5) f 21 31 r compact 0.01 2.24 0.00 -0.51
2.4 10.69 12.34 11.96 12.71 -1.64 toyota camry solara 2008 4 auto(s5) f 22 31 r compact 0.01 2.24 0.00 -0.74
3.0 13.07 13.74 13.43 14.05 -0.67 toyota camry solara 1999 6 auto(l4) f 18 26 r compact 0.00 2.24 0.00 -0.30
3.0 13.07 13.74 13.43 14.05 -0.67 toyota camry solara 1999 6 manual(m5) f 18 26 r compact 0.00 2.24 0.00 -0.30
3.3 13.07 14.44 14.15 14.73 -1.37 toyota camry solara 2008 6 auto(s5) f 18 27 r compact 0.00 2.24 0.00 -0.61
1.8 9.80 10.93 10.46 11.40 -1.13 toyota corolla 1999 4 auto(l3) f 24 30 r compact 0.01 2.24 0.00 -0.51
1.8 9.80 10.93 10.46 11.40 -1.13 toyota corolla 1999 4 auto(l4) f 24 33 r compact 0.01 2.24 0.00 -0.51
1.8 9.05 10.93 10.46 11.40 -1.89 toyota corolla 1999 4 manual(m5) f 26 35 r compact 0.01 2.24 0.00 -0.85
1.8 8.40 10.93 10.46 11.40 -2.53 toyota corolla 2008 4 manual(m5) f 28 37 r compact 0.01 2.24 0.01 -1.14
1.8 9.05 10.93 10.46 11.40 -1.89 toyota corolla 2008 4 auto(l4) f 26 35 r compact 0.01 2.24 0.00 -0.85
4.7 21.38 17.71 17.31 18.11 3.67 toyota land cruiser wagon 4wd 1999 8 auto(l4) 4 11 15 r suv 0.01 2.23 0.01 1.65
5.7 18.09 20.05 19.48 20.63 -1.96 toyota land cruiser wagon 4wd 2008 8 auto(s6) 4 13 18 r suv 0.02 2.24 0.01 -0.88
2.7 15.68 13.04 12.70 13.37 2.64 toyota toyota tacoma 4wd 1999 4 manual(m5) 4 15 20 r pickup 0.01 2.24 0.00 1.18
2.7 14.70 13.04 12.70 13.37 1.66 toyota toyota tacoma 4wd 1999 4 auto(l4) 4 16 20 r pickup 0.01 2.24 0.00 0.75
2.7 13.84 13.04 12.70 13.37 0.80 toyota toyota tacoma 4wd 2008 4 manual(m5) 4 17 22 r pickup 0.01 2.24 0.00 0.36
3.4 15.68 14.67 14.38 14.96 1.01 toyota toyota tacoma 4wd 1999 6 manual(m5) 4 15 17 r pickup 0.00 2.24 0.00 0.45
3.4 15.68 14.67 14.38 14.96 1.01 toyota toyota tacoma 4wd 1999 6 auto(l4) 4 15 19 r pickup 0.00 2.24 0.00 0.45
4.0 15.68 16.08 15.76 16.39 -0.40 toyota toyota tacoma 4wd 2008 6 manual(m6) 4 15 18 r pickup 0.00 2.24 0.00 -0.18
4.0 14.70 16.08 15.76 16.39 -1.38 toyota toyota tacoma 4wd 2008 6 auto(l5) 4 16 20 r pickup 0.00 2.24 0.00 -0.62
2.0 11.20 11.40 10.96 11.84 -0.20 volkswagen gti 1999 4 manual(m5) f 21 29 r compact 0.01 2.24 0.00 -0.09
2.0 12.38 11.40 10.96 11.84 0.98 volkswagen gti 1999 4 auto(l4) f 19 26 r compact 0.01 2.24 0.00 0.44
2.0 11.20 11.40 10.96 11.84 -0.20 volkswagen gti 2008 4 manual(m6) f 21 29 p compact 0.01 2.24 0.00 -0.09
2.0 10.69 11.40 10.96 11.84 -0.71 volkswagen gti 2008 4 auto(s6) f 22 29 p compact 0.01 2.24 0.00 -0.32
2.8 13.84 13.27 12.95 13.60 0.57 volkswagen gti 1999 6 manual(m5) f 17 24 r compact 0.01 2.24 0.00 0.25
1.9 7.13 11.17 10.71 11.62 -4.04 volkswagen jetta 1999 4 manual(m5) f 33 44 d compact 0.01 2.23 0.02 -1.81
2.0 11.20 11.40 10.96 11.84 -0.20 volkswagen jetta 1999 4 manual(m5) f 21 29 r compact 0.01 2.24 0.00 -0.09
2.0 12.38 11.40 10.96 11.84 0.98 volkswagen jetta 1999 4 auto(l4) f 19 26 r compact 0.01 2.24 0.00 0.44
2.0 10.69 11.40 10.96 11.84 -0.71 volkswagen jetta 2008 4 auto(s6) f 22 29 p compact 0.01 2.24 0.00 -0.32
2.0 11.20 11.40 10.96 11.84 -0.20 volkswagen jetta 2008 4 manual(m6) f 21 29 p compact 0.01 2.24 0.00 -0.09
2.5 11.20 12.57 12.21 12.93 -1.37 volkswagen jetta 2008 5 auto(s6) f 21 29 r compact 0.01 2.24 0.00 -0.61
2.5 11.20 12.57 12.21 12.93 -1.37 volkswagen jetta 2008 5 manual(m5) f 21 29 r compact 0.01 2.24 0.00 -0.61
2.8 14.70 13.27 12.95 13.60 1.43 volkswagen jetta 1999 6 auto(l4) f 16 23 r compact 0.01 2.24 0.00 0.64
2.8 13.84 13.27 12.95 13.60 0.57 volkswagen jetta 1999 6 manual(m5) f 17 24 r compact 0.01 2.24 0.00 0.25
1.9 6.72 11.17 10.71 11.62 -4.45 volkswagen new beetle 1999 4 manual(m5) f 35 44 d subcompact 0.01 2.22 0.02 -2.00
1.9 8.11 11.17 10.71 11.62 -3.06 volkswagen new beetle 1999 4 auto(l4) f 29 41 d subcompact 0.01 2.23 0.01 -1.37
2.0 11.20 11.40 10.96 11.84 -0.20 volkswagen new beetle 1999 4 manual(m5) f 21 29 r subcompact 0.01 2.24 0.00 -0.09
2.0 12.38 11.40 10.96 11.84 0.98 volkswagen new beetle 1999 4 auto(l4) f 19 26 r subcompact 0.01 2.24 0.00 0.44
2.5 11.76 12.57 12.21 12.93 -0.81 volkswagen new beetle 2008 5 manual(m5) f 20 28 r subcompact 0.01 2.24 0.00 -0.36
2.5 11.76 12.57 12.21 12.93 -0.81 volkswagen new beetle 2008 5 auto(s6) f 20 29 r subcompact 0.01 2.24 0.00 -0.36
1.8 11.20 10.93 10.46 11.40 0.27 volkswagen passat 1999 4 manual(m5) f 21 29 p midsize 0.01 2.24 0.00 0.12
1.8 13.07 10.93 10.46 11.40 2.14 volkswagen passat 1999 4 auto(l5) f 18 29 p midsize 0.01 2.24 0.01 0.96
2.0 12.38 11.40 10.96 11.84 0.98 volkswagen passat 2008 4 auto(s6) f 19 28 p midsize 0.01 2.24 0.00 0.44
2.0 11.20 11.40 10.96 11.84 -0.20 volkswagen passat 2008 4 manual(m6) f 21 29 p midsize 0.01 2.24 0.00 -0.09
2.8 14.70 13.27 12.95 13.60 1.43 volkswagen passat 1999 6 auto(l5) f 16 26 p midsize 0.01 2.24 0.00 0.64
2.8 13.07 13.27 12.95 13.60 -0.20 volkswagen passat 1999 6 manual(m5) f 18 26 p midsize 0.01 2.24 0.00 -0.09
3.6 13.84 15.14 14.85 15.43 -1.30 volkswagen passat 2008 6 auto(s6) f 17 26 p midsize 0.00 2.24 0.00 -0.58

Same methods for other model types

augment(m2, newdata = new_data, interval = "prediction") |>
  kable(digits = 2)
displ .fitted .lower .upper
1.6 9.19 4.94 13.45
2.1 11.20 6.97 15.42
2.6 12.98 8.77 17.19
3.1 14.55 10.33 18.76
3.6 15.89 11.67 20.11
4.1 17.02 12.80 21.24
4.6 17.93 13.71 22.15
5.1 18.62 14.40 22.84
5.6 19.09 14.85 23.34
6.1 19.35 15.05 23.64
6.6 19.38 14.98 23.78
7.1 19.20 14.62 23.78

Same methods for other model types

new_data2 = tibble(logGDPpercap = seq(2.3, 5.0, 0.25))
augment(m3, newdata = new_data2, 
        interval = "prediction", level = 0.90) |>
   kable(digits = 2)
logGDPpercap .fitted .lower .upper
2.30 35.41 20.44 50.38
2.55 40.25 25.29 55.21
2.80 45.09 30.13 60.05
3.05 49.93 34.97 64.88
3.30 54.77 39.82 69.72
3.55 59.60 44.65 74.55
3.80 64.44 49.49 79.39
4.05 69.28 54.33 84.23
4.30 74.12 59.16 89.08
4.55 78.96 63.99 93.92
4.80 83.80 68.82 98.77

Same methods for other model types

augment(m4, newdata = new_data, interval = "confidence") |> kable(digits = 2)
displ .tau .fitted .lower .upper
1.6 0.5 10.21 9.77 10.65
2.1 0.5 11.45 11.10 11.80
2.6 0.5 12.68 12.39 12.97
3.1 0.5 13.92 13.63 14.20
3.6 0.5 15.15 14.82 15.49
4.1 0.5 16.39 15.97 16.81
4.6 0.5 17.62 17.11 18.14
5.1 0.5 18.86 18.23 19.49
5.6 0.5 20.10 19.35 20.85
6.1 0.5 21.33 20.46 22.20
6.6 0.5 22.57 21.57 23.56
7.1 0.5 23.80 22.68 24.92

Summary

  • Fitting regression models (lines, polynomials, transformations) to means and quantiles

  • Extracting model coefficients, uncertainties, errors (with tidy)

  • Computing predicted values (with two kinds of errors) and residuals (compared to data)

  • Most models can’t make predictions from NA. NAs in data can cause problems.

Further reading

  • Course notes

  • Healy Chapter 6. Work with models.