Question

The following Excel output is from an analysis of the Appraised Value for tax purposes of homes in a suburban location. The three independent variables are: Property Size, House Size and Age of the house. The average Appraised Value (in thousands of dollars) is 398.

Regression Statistics
Multiple R	0.91
R Square	0.83
Adjusted R Square	0.81
Standard Error	22.48
Observations	30.00
ANOVA
	df	SS	MS	F	Significance F
Regression	3.00	348699.01	116233.00	42.20	0.00
Residual	26.00	71606.53	2754.10
Total	29.00	420305.54
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	136.79	53.83	2.54	0.02	26.15	247.44
Property Size (acres)	276.09	78.20	3.53	0.00	115.35	436.82
House Size (sq. feet)	0.13	0.02	6.16	0.00	0.09	0.17
Age	-1.40	0.48	-2.94	0.01	-2.38	-0.42

Can we be confident that this constitutes an acceptable regression to predict appraised value from the three independent variables of property size, house size and age? Why or why not? You must indicate your reasoning to get credit for this problem.

Answer 1

Please don't hesitate to give a "thumbs up" in case you're satisfied with the answer

It is an acceptable regression if the following conditions are met:

1. overall regression equation is statistically significant.

in our case p-value is less than .05, indicating that linear model is statistically significant

2. at least one of the variables is statistically significant

in our case, Yes, we have all variables are statistically significant as all have less than .05 p-value

3. R-Square should be high, at 0.83 it is high indicating good predictive strength of the predictor variables.

Overall, we be confident that this constitutes an acceptable regression to predict appraised value from the three independent variables of property size, house size and age