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. "

Selling Prices of Houses


Price Sqft Brick (1 if brick, 0 if otherwise)


194461 2006 1


156020 1613 0


252256 3574 1


236633 3599 0


185924 1857 1


193210 2332 0


228162 3608 0


194161 2327 0


208608 2579 1


213552 2846 0


181635 1826 1


175377 1788 0


235672 3251 0


178035 1868 1


194800 2245 1


172700 1480 1


190242 1925 1


261082 3594 0


188270 2022 1


188840 2284 0

Answer 1

This is regression analysis in Data analysis.

Here we have two independent variables: Sq ft areas (X1), and the other (X2) is "whether made of bricks or not." The price is the dependent variable Y.

The parameters (coefficients) of the regression equation are as follows :

Y-intercept (Price) = 99689.20 units.

Coefficient of 'Sq ft area' variable = 39.86 units.

Coefficient of 'Brick' variable = 9779.10 units.

Regression equation :

Price = 99689.20 + 39.86 Area_in_Sqft + 9779.10 Brick.

Hypothesis testing:

On performing the t-test we obtain the P-value of 0.013 and it's less than the confidence level 0.05 set for the hypothesis.

Regarding the claim/hypothesis:

there is 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.

Answer 2

Answer: Regression Equation (rounded to two decimal places):

Price = 139974.98 + 35.80 * Sqft + 14617.62 * Brick

Explanation:

To determine if there is enough evidence to support the claim that brick houses are more expensive than other types of houses at the 0.05 level of significance, we can perform a regression analysis using statistical software.

Using the data provided, the regression equation is:

Price = 139974.98 + 35.80 * Sqft + 14617.62 * Brick

The coefficient of the "Brick" variable is 14617.62, which suggests that on average, brick houses are associated with a higher selling price by $14617.62 compared to non-brick houses, after controlling for the square footage.

To determine if there is enough evidence to support the claim, we need to perform a hypothesis test. The null hypothesis (H0) is that there is no difference in average selling prices between brick houses and non-brick houses (β2 = 0). The alternative hypothesis (Ha) is that there is a difference in average selling prices (β2 ≠ 0).

We can perform a t-test on the coefficient of the "Brick" variable, and if the p-value is less than 0.05 (the significance level), we reject the null hypothesis and conclude that there is enough evidence to support the claim.

Performing the t-test, we find that the p-value for the "Brick" variable is less than 0.05. Therefore, we reject the null hypothesis and conclude that there is enough evidence to support the claim that on average, brick houses are more expensive than other types of houses.

Regression Equation (rounded to two decimal places):

Price = 139974.98 + 35.80 * Sqft + 14617.62 * Brick