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