R Markdown
Cars Example - Part 1: Setup the files
## mpg cyl disp hp drat wt qsec vs am gear carb
## 1 21.0 6 160.0 110 3.90 2.620 16.46 0 1 4 4
## 2 21.0 6 160.0 110 3.90 2.875 17.02 0 1 4 4
## 3 22.8 4 108.0 93 3.85 2.320 18.61 1 1 4 1
## 4 21.4 6 258.0 110 3.08 3.215 19.44 1 0 3 1
## 5 18.7 8 360.0 175 3.15 3.440 17.02 0 0 3 2
## 6 18.1 6 225.0 105 2.76 3.460 20.22 1 0 3 1
## 7 14.3 8 360.0 245 3.21 3.570 15.84 0 0 3 4
## 8 24.4 4 146.7 62 3.69 3.190 20.00 1 0 4 2
## 9 22.8 4 140.8 95 3.92 3.150 22.90 1 0 4 2
## 10 19.2 6 167.6 123 3.92 3.440 18.30 1 0 4 4
## 11 17.8 6 167.6 123 3.92 3.440 18.90 1 0 4 4
## 12 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 3
## 13 17.3 8 275.8 180 3.07 3.730 17.60 0 0 3 3
## 14 15.2 8 275.8 180 3.07 3.780 18.00 0 0 3 3
## 15 10.4 8 472.0 205 2.93 5.250 17.98 0 0 3 4
## 16 10.4 8 460.0 215 3.00 5.424 17.82 0 0 3 4
## 17 14.7 8 440.0 230 3.23 5.345 17.42 0 0 3 4
## 18 32.4 4 78.7 66 4.08 2.200 19.47 1 1 4 1
## 19 30.4 4 75.7 52 4.93 1.615 18.52 1 1 4 2
## 20 33.9 4 71.1 65 4.22 1.835 19.90 1 1 4 1
## 21 21.5 4 120.1 97 3.70 2.465 20.01 1 0 3 1
## 22 15.5 8 318.0 150 2.76 3.520 16.87 0 0 3 2
## 23 15.2 8 304.0 150 3.15 3.435 17.30 0 0 3 2
## 24 13.3 8 350.0 245 3.73 3.840 15.41 0 0 3 4
## 25 19.2 8 400.0 175 3.08 3.845 17.05 0 0 3 2
## 26 27.3 4 79.0 66 4.08 1.935 18.90 1 1 4 1
## 27 26.0 4 120.3 91 4.43 2.140 16.70 0 1 5 2
## 28 30.4 4 95.1 113 3.77 1.513 16.90 1 1 5 2
## 29 15.8 8 351.0 264 4.22 3.170 14.50 0 1 5 4
## 30 19.7 6 145.0 175 3.62 2.770 15.50 0 1 5 6
## 31 15.0 8 301.0 335 3.54 3.570 14.60 0 1 5 8
## 32 21.4 4 121.0 109 4.11 2.780 18.60 1 1 4 2
Cars Example - Part 2: Pairs Plot
Cars Example - Part 3: Hypothesis Testing
## [1] -0.8676594
## Loading required package: ggplot2
Cars Example - Part 4: Summary of details
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 37.285126 1.877627 19.857575 8.241799e-19
## wt -5.344472 0.559101 -9.559044 1.293959e-10
## [1] "R-squared" "0.75"
Cars Example - Part 5: Test other correlations
## Start: AIC=70.9
## mpg ~ cyl + disp + hp + drat + wt + qsec + vs + am + gear + carb
##
## Df Sum of Sq RSS AIC
## - cyl 1 0.0799 147.57 68.915
## - vs 1 0.1601 147.66 68.932
## - carb 1 0.4067 147.90 68.986
## - gear 1 1.3531 148.85 69.190
## - drat 1 1.6270 149.12 69.249
## - disp 1 3.9167 151.41 69.736
## - hp 1 6.8399 154.33 70.348
## - qsec 1 8.8641 156.36 70.765
## <none> 147.49 70.898
## - am 1 10.5467 158.04 71.108
## - wt 1 27.0144 174.51 74.280
##
## Step: AIC=68.92
## mpg ~ disp + hp + drat + wt + qsec + vs + am + gear + carb
##
## Df Sum of Sq RSS AIC
## - vs 1 0.2685 147.84 66.973
## - carb 1 0.5201 148.09 67.028
## - gear 1 1.8211 149.40 67.308
## - drat 1 1.9826 149.56 67.342
## - disp 1 3.9009 151.47 67.750
## - hp 1 7.3632 154.94 68.473
## <none> 147.57 68.915
## - qsec 1 10.0933 157.67 69.032
## - am 1 11.8359 159.41 69.384
## - wt 1 27.0280 174.60 72.297
##
## Step: AIC=66.97
## mpg ~ disp + hp + drat + wt + qsec + am + gear + carb
##
## Df Sum of Sq RSS AIC
## - carb 1 0.6855 148.53 65.121
## - gear 1 2.1437 149.99 65.434
## - drat 1 2.2139 150.06 65.449
## - disp 1 3.6467 151.49 65.753
## - hp 1 7.1060 154.95 66.475
## <none> 147.84 66.973
## - am 1 11.5694 159.41 67.384
## - qsec 1 15.6830 163.53 68.200
## - wt 1 27.3799 175.22 70.410
##
## Step: AIC=65.12
## mpg ~ disp + hp + drat + wt + qsec + am + gear
##
## Df Sum of Sq RSS AIC
## - gear 1 1.565 150.09 63.457
## - drat 1 1.932 150.46 63.535
## <none> 148.53 65.121
## - disp 1 10.110 158.64 65.229
## - am 1 12.323 160.85 65.672
## - hp 1 14.826 163.35 66.166
## - qsec 1 26.408 174.94 68.358
## - wt 1 69.127 217.66 75.350
##
## Step: AIC=63.46
## mpg ~ disp + hp + drat + wt + qsec + am
##
## Df Sum of Sq RSS AIC
## - drat 1 3.345 153.44 62.162
## - disp 1 8.545 158.64 63.229
## <none> 150.09 63.457
## - hp 1 13.285 163.38 64.171
## - am 1 20.036 170.13 65.466
## - qsec 1 25.574 175.67 66.491
## - wt 1 67.572 217.66 73.351
##
## Step: AIC=62.16
## mpg ~ disp + hp + wt + qsec + am
##
## Df Sum of Sq RSS AIC
## - disp 1 6.629 160.07 61.515
## <none> 153.44 62.162
## - hp 1 12.572 166.01 62.682
## - qsec 1 26.470 179.91 65.255
## - am 1 32.198 185.63 66.258
## - wt 1 69.043 222.48 72.051
##
## Step: AIC=61.52
## mpg ~ hp + wt + qsec + am
##
## Df Sum of Sq RSS AIC
## - hp 1 9.219 169.29 61.307
## <none> 160.07 61.515
## - qsec 1 20.225 180.29 63.323
## - am 1 25.993 186.06 64.331
## - wt 1 78.494 238.56 72.284
##
## Step: AIC=61.31
## mpg ~ wt + qsec + am
##
## Df Sum of Sq RSS AIC
## <none> 169.29 61.307
## - am 1 26.178 195.46 63.908
## - qsec 1 109.034 278.32 75.217
## - wt 1 183.347 352.63 82.790
Cars Example - Part 6: get the best model
## lm(formula = mpg ~ wt + qsec + am, data = cars_data)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 9.617781 6.9595930 1.381946 1.779152e-01
## wt -3.916504 0.7112016 -5.506882 6.952711e-06
## factor(am)1 2.935837 1.4109045 2.080819 4.671551e-02
## qsec 1.225886 0.2886696 4.246676 2.161737e-04
## [1] "R-squared" "0.85"