Question

Suppose the following data were collected relating the selling price of a house to square footage and whether or not the house is made out of brick. Use statistical software to find the regression equation. Is there enough evidence to support the claim that on average brick houses are more expensive than other types of houses at the 0.05 level of significance? If yes, type the regression equation in the spaces provided with answers rounded to two decimal places. Else, select "There is not enough evidence."

I could not get the entire table in 1 picture so I took 2 pictures

These are the numbers from the 2nd picture in case they are too small

226069	3263	0
186387	2258	0
204800	2495	1
214960	2772	0

Selling Prices of Houses Price Sqft Brick (1 if brick, O if otherwise) 233345 3526 244243 3427 2103532717 2153632919 166225 1342 2126612838 205273 2507 222408 2884 1511251650 1679331908 2425923516 240660 3399 1928202080 1999012497 1700401515 238768 3503 0 0 226069 3263 186387 2258 204800 2495 214960 2772 0 0 0 EEB Tables Answer How to enter your answer Selecting a checkbox will replace the entered answer value(s) with the checkbox value. If the checkbox is not selected, the entered answer is used PRICE SQFT+ BRICK e There is not enough evidence

Answer 1

Solution:

Here, we have to develop a regression model for the prediction of the dependent variable price based on the independent variables sqft and Brick. The required regression model by using excel is given as below:

Regression Statistics
Multiple R	0.977198575
R Square	0.954917055
Adjusted R Square	0.949613179
Standard Error	6228.160973
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	2	13967605236	6983802618	180.0413658	3.6233E-12
Residual	17	659429814.7	38789989.1
Total	19	14627035050
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	106558.0743	5751.587409	18.52672432	1.0411E-12	94423.28574	118692.8629
Sqft	36.60749499	2.28493242	16.02125939	1.08392E-11	31.78670902	41.42828096
Brick	7398.155862	3076.330574	2.404863744	0.027851055	907.6657545	13888.64597

The p-value for this regression model is given as 3.6233E-12 ≈ 0.00 which is less than alpha value 0.05, so we reject the null hypothesis. There is sufficient evidence to conclude that the given regression model is statistically significant for the prediction of the dependent variable price.

The required regression equation is given as below:

PRICE_i = 106558.07 + 36.61*SQFT_i + 7398.16*BRICK_i + e_i