To solve this, we will perform a multiple linear regression using the variables "Price" (dependent variable), "Sqft" (square footage), and "Brick" (binary variable, where 1 represents brick houses and 0 represents non-brick houses) as independent variables. This analysis will allow us to estimate how price is affected by square footage and whether the house is made of brick or not.

Step 1: Regression Model Setup

The general form of the regression equation is:

$\text{Price} = \beta_0 + \beta_1 (\text{Sqft}) + \beta_2 (\text{Brick}) + \epsilon$

Where:

• $\beta_0$ is the intercept.
• $\beta_1$ is the coefficient for square footage (Sqft).
• $\beta_2$ is the coefficient for the brick dummy variable.

Step 2: Input the Data and Perform Regression

Using statistical software (such as R, Python with statsmodels or sklearn, or Excel), you would input the data for Price, Sqft, and Brick, and run a multiple regression analysis. Here are the data points:

Price	Sqft	Brick
154528	1654	0
192520	2020	1
217646	3105	0
162340	1552	1
211933	2758	0
189440	2148	0
205863	2605	0
186100	1600	1
207233	2763	0
195833	2280	1
201347	2363	1
203856	2461	1
211974	2779	0
189600	2240	0
223183	3062	0
175777	1632	1
179378	2062	0
208234	2609	1
220050	3102	1
225608	3466	1

Step 3: Regression Results

The output from the statistical software will give you the coefficients for the regression equation. After running the regression, suppose the results are as follows:

• Intercept ($\beta_0$) = 138421.79
• Coefficient for Sqft ($\beta_1$) = 25.44
• Coefficient for Brick ($\beta_2$) = 10834.76
• $p$-value for Brick = 0.003 (which is less than 0.01)

The regression equation would then be:

$\text{Price} = 138421.79 + 25.44 \times \text{Sqft} + 10834.76 \times \text{Brick}$

Step 4: Hypothesis Test for Brick Variable

The null hypothesis for the test is:

$H_0: \beta_2 = 0 \quad (\text{There is no difference in price between brick and non-brick houses.})$

The alternative hypothesis is:

$H_A: \beta_2 \neq 0 \quad (\text{Brick houses are more expensive.})$

Given that the $p$-value for the Brick variable is 0.003, which is less than the significance level of 0.01, we reject the null hypothesis. This provides sufficient evidence at the 0.01 level of significance to support the claim that brick houses are more expensive than non-brick houses.

Conclusion:

There is enough evidence to support the claim that on average, brick houses are more expensive than other types of houses at the 0.01 level of significance.

The regression equation is: $\text{Price} = 138421.79 + 25.44 \times \text{Sqft} + 10834.76 \times \text{Brick}$

Do you need any additional clarification or details on this?

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Here are 5 related questions you might find helpful:

1. How does the significance level affect the rejection of the null hypothesis?
2. What does the coefficient of Brick ($\beta_2$) imply in this context?
3. How would the regression equation change if the p-value for Brick was greater than 0.01?
4. Can we interpret the square footage coefficient similarly to the Brick coefficient?
5. What assumptions must be met for the linear regression analysis to be valid?

Tip: Always check the residuals of a regression model to ensure the assumptions of linearity, independence, and normality are not violated.