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 |
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 |
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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:
PRICEi = 106558.07 + 36.61*SQFTi + 7398.16*BRICKi + ei
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