Question

The following data was collected to explore how the number of square feet in a house, the number of bedrooms, and the age of the house affect the selling price of the house. The dependent variable is the selling price of the house, the first independent variable (x1) is the square footage, the second independent variable (x2) is the number of bedrooms, and the third independent variable (x3) is the age of the house. Effects on Selling Price of Houses Square Feet Number of Bedrooms Age Selling Price 3073 5 15 282300 2961 4 14 231300 2082 4 14 203900 1725 4 10 185400 1700 4 9 181200 1529 3 8 172700 1388 3 8 170500 1083 3 7 165900 1030 3 5 107300

Step 2 of 2 : Determine if a statistically significant linear relationship exists between the independent and dependent variables at the 0.05 level of significance. If the relationship is statistically significant, identify the multiple regression equation that best fits the data, rounding the answers to three decimal places. Otherwise, indicate that there is not enough evidence to show that the relationship is statistically significant.

Answer 1

Results from excel

Goto Data mennu ---> Data Analysis ---> Regression

Select the X range and Y range click on labels and click OK.

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.941
R Square	0.885
Adjusted R Square	0.816
Standard Error	20699.691
Observations	9

ANOVA
	df	SS	MS	F	p-value
Regression	3	16464016180	5488005393	12.80816	0.008779
Residual	5	2142386042	428477208.5
Total	8	18606402222

Since p-value is less than level of significance (0.05) we reject null hypothesis that there is no significant linear relationship between dependent and independent variables. Thus we we conclude that a statistically significant linear relationship exists between the independent and dependent variables at the 0.05 level of significance.

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	44303.310	47014.412	0.942	0.389	-76551.084	165157.703
Square Feet	30.177	29.100	1.037	0.347	-44.627	104.981
Number of Bedrooms	11790.306	20582.630	0.573	0.592	-41119.028	64699.641
Age	4584.684	6097.084	0.752	0.486	-11088.370	20257.737

Equation is Selling price = 44303.310 +30.177 Square Feet+11790.306 Number of Bedrooms+4584.684 Age