Question: Model Summary - mpg Model R R Adjusted R RMSE 1 0.000 0.000 0.000 4.294 2 0.818 0.670 0.668 2.476 3 0.840 0.705 0.701 2.348

Model Summary - mpg
Model R R Adjusted R RMSE
1 0.000 0.000 0.000 4.294
2 0.818 0.670 0.668 2.476
3 0.840 0.705 0.701 2.348
4 0.857 0.734 0.728 2.238
5 0.865 0.749 0.742 2.180
ANOVA
Model Sum of Squares df Mean Square F p
2 Regression 1877.288 1 1877.288 306.273 <.001
Residual 925.549 151 6.129
Total 2802.837 152
3 Regression 1975.593 2 987.796 179.112 <.001
Residual 827.244 150 5.515
Total 2802.837 152
4 Regression 2056.374 3 685.458 136.823 <.001
Residual 746.463 149 5.010
Total 2802.837 152
5 Regression 2099.452 4 524.863 110.437 <.001
Residual 703.385 148 4.753
Total 2802.837 152
Note.The intercept model is omitted, as no meaningful information can be shown.
Coefficients
Model Unstandardized Standard Error Standardized t p
1 (Intercept) 23.856 0.347 68.718 <.001
2 (Intercept) 42.558 1.087 39.144 <.001
curb_wgt -5.538 0.316 -0.818 -17.501 <.001
3 (Intercept) 42.516 1.031 41.224 <.001
curb_wgt -3.358 0.597 -0.496 -5.622 <.001
fuel_cap -0.408 0.097 -0.373 -4.222 <.001
4 (Intercept) 41.242 1.033 39.927 <.001
curb_wgt -2.064 0.654 -0.305 -3.154 0.002
fuel_cap -0.398 0.092 -0.364 -4.320 <.001
engine_s -1.074 0.267 -0.262 -4.016 <.001
5 (Intercept) 33.804 2.667 12.673 <.001
curb_wgt -2.534 0.656 -0.374 -3.862 <.001
fuel_cap -0.415 0.090 -0.379 -4.619 <.001
engine_s -1.172 0.263 -0.286 -4.464 <.001
length 0.052 0.017 0.161 3.011 0.003
Note.The following covariates were considered but not included: horsepow, wheelbas, width.

Based on the above results answer the following questions:

  1. Determine the best fitted regression model.
  2. Write the equation of the regression model (best -fit model) and interpret all the Beta coefficients.
  3. Interpret the ANOVA for regression fit.
  4. Determine and interpret the coefficient of determination r2.
  5. What can we conclude about the relationship of the dependent and predictor variables?

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