Model Summary - mpg
Model	R	R	Adjusted R	RMSE	R Change	F Change	df1	df2	p
1		0.000		0.000		0.000		4.294		0.000				0		152
2		0.818		0.670		0.668		2.476		0.670		306.273		1		151		<.001
3		0.840		0.705		0.701		2.348		0.035		17.825		1		150		<.001
4		0.857		0.734		0.728		2.238		0.029		16.125		1		149		<.001
5		0.865		0.749		0.742		2.180		0.015		9.064		1		148		0.003

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
	Collinearity Statistics
Model		Unstandardized	Standard Error	Standardized	t	p	Tolerance	VIF
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		1.000		1.000
3		(Intercept)		42.516		1.031				41.224		<.001
		curb_wgt		-3.358		0.597		-0.496		-5.622		<.001		0.253		3.959
		fuel_cap		-0.408		0.097		-0.373		-4.222		<.001		0.253		3.959
4		(Intercept)		41.242		1.033				39.927		<.001
		curb_wgt		-2.064		0.654		-0.305		-3.154		0.002		0.191		5.229
		fuel_cap		-0.398		0.092		-0.364		-4.320		<.001		0.252		3.962
		engine_s		-1.074		0.267		-0.262		-4.016		<.001		0.421		2.377
5		(Intercept)		33.804		2.667				12.673		<.001
		curb_wgt		-2.534		0.656		-0.374		-3.862		<.001		0.180		5.544
		fuel_cap		-0.415		0.090		-0.379		-4.619		<.001		0.251		3.978
		engine_s		-1.172		0.263		-0.286		-4.464		<.001		0.414		2.414
		length		0.052		0.017		0.161		3.011		0.003		0.592		1.689
Note.The following covariates were considered but not included: horsepow, wheelbas, width.

Descriptives
	N	Mean	SD	SE
mpg		153		23.856		4.294		0.347
engine_s		153		3.050		1.046		0.085
horsepow		153		185.072		56.729		4.586
wheelbas		153		107.410		7.693		0.622
width		153		71.086		3.453		0.279
length		153		187.092		13.433		1.086
curb_wgt		153		3.377		0.635		0.051
fuel_cap		153		17.954		3.925		0.317

Collinearity Diagnostics
	Variance Proportions
Model	Dimension	Eigenvalue	Condition Index	(Intercept)	engine_s	length	curb_wgt	fuel_cap
2		1		1.983		1.000		0.009						0.009
		2		0.017		10.771		0.991						0.991
3		1		2.970		1.000		0.004						0.001		0.001
		2		0.025		10.827		0.869						0.027		0.123
		3		0.005		23.993		0.127						0.972		0.876
4		1		3.923		1.000		0.002		0.003				0.000		0.001
		2		0.054		8.489		0.226		0.477				0.000		0.001
		3		0.018		14.861		0.550		0.367				0.023		0.302
		4		0.005		29.517		0.222		0.153				0.976		0.696
5		1		4.909		1.000		0.000		0.002		0.000		0.000		0.000
		2		0.065		8.682		0.017		0.395		0.006		0.000		0.001
		3		0.020		15.846		0.028		0.435		0.010		0.031		0.302
		4		0.005		33.010		0.025		0.147		0.000		0.927		0.696
		5		0.002		51.785		0.929		0.021		0.984		0.042		0.001
Note.The intercept model is omitted, as no meaningful information can be shown.

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?