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 (x) 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 2848 4 6 242100 1270 5 7 113600 1825 4 281700 2235 199100 2072 4 307500 2197 4 14 278800 2184 5. 275300 Prev 1764 4 7 107200 2276 4 14 103000 Copy Data Step 1 of 2: Find the p-value for the regression equation that fits the given data. Round your answer to four decimal places.

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### Linear Regression Analysis on Housing Data

The table below presents data on house characteristics and their selling prices. The goal is to determine if there is a statistically significant linear relationship between the independent variables (Square Feet, Number of Bedrooms, Age) and the dependent variable (Selling Price) at the 0.05 level of significance. If significant, we will identify the multiple regression equation that best fits the data.

| Square Feet | Number of Bedrooms | Age | Selling Price |
|-------------|---------------------|-----|---------------|
| 2848        | 4                   | 6   | 242100        |
| 1270        | 4                   | 7   | 113600        |
| 1825        | 4                   | 8   | 281700        |
| 2235        | 5                   | 5   | 199100        |
| 2072        | 4                   | 2   | 307500        |
| 2197        | 4                   | 14  | 278800        |
| 2184        | 4                   | 5   | 275300        |
| 1764        | 4                   | 7   | 107200        |
| 2276        | 4                   | 14  | 103000        |

#### Step 2 of 2

Determine whether there is a statistically significant linear relationship at the 0.05 significance level.

If the relationship is confirmed as statistically significant, you will need to compute the multiple regression equation that best fits the data, rounding the answers to three decimal places. Otherwise, indicate that there is not enough evidence for statistical significance.

Use the regression equation form:
\[ \hat{y} = b_0 + b_1 x_1 + b_2 x_2 + b_3 x_3 \]

- \( b_0 \): Intercept
- \( b_1 \), \( b_2 \), \( b_3 \): Coefficients for Square Feet, Number of Bedrooms, and Age respectively

To proceed, select the appropriate checkbox if there is enough evidence, otherwise note that there isn't.
Transcribed Image Text:### Linear Regression Analysis on Housing Data The table below presents data on house characteristics and their selling prices. The goal is to determine if there is a statistically significant linear relationship between the independent variables (Square Feet, Number of Bedrooms, Age) and the dependent variable (Selling Price) at the 0.05 level of significance. If significant, we will identify the multiple regression equation that best fits the data. | Square Feet | Number of Bedrooms | Age | Selling Price | |-------------|---------------------|-----|---------------| | 2848 | 4 | 6 | 242100 | | 1270 | 4 | 7 | 113600 | | 1825 | 4 | 8 | 281700 | | 2235 | 5 | 5 | 199100 | | 2072 | 4 | 2 | 307500 | | 2197 | 4 | 14 | 278800 | | 2184 | 4 | 5 | 275300 | | 1764 | 4 | 7 | 107200 | | 2276 | 4 | 14 | 103000 | #### Step 2 of 2 Determine whether there is a statistically significant linear relationship at the 0.05 significance level. If the relationship is confirmed as statistically significant, you will need to compute the multiple regression equation that best fits the data, rounding the answers to three decimal places. Otherwise, indicate that there is not enough evidence for statistical significance. Use the regression equation form: \[ \hat{y} = b_0 + b_1 x_1 + b_2 x_2 + b_3 x_3 \] - \( b_0 \): Intercept - \( b_1 \), \( b_2 \), \( b_3 \): Coefficients for Square Feet, Number of Bedrooms, and Age respectively To proceed, select the appropriate checkbox if there is enough evidence, otherwise note that there isn't.
### Exploring the Factors Affecting the Selling Price of Houses

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 (\(x_1\)) is the square footage, the second independent variable (\(x_2\)) is the number of bedrooms, and the third independent variable (\(x_3\)) is the age of the house.

#### Effects on Selling Price of Houses

| Square Feet | Number of Bedrooms | Age | Selling Price |
|-------------|---------------------|-----|---------------|
| 2848        | 4                   | 6   | $242,100      |
| 1270        | 5                   | 7   | $113,600      |
| 1825        | 4                   | 8   | $281,700      |
| 2235        | 5                   | 5   | $199,100      |
| 2072        | 4                   | 2   | $307,500      |
| 2197        | 4                   | 14  | $278,800      |
| 2184        | 4                   | 5   | $275,300      |
| 1764        | 4                   | 7   | $107,200      |
| 2276        | 4                   | 14  | $103,000      |

**Instructions:**

Step 1 of 2: Find the \(p\)-value for the regression equation that fits the given data. Round your answer to four decimal places.
Transcribed Image Text:### Exploring the Factors Affecting the Selling Price of Houses 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 (\(x_1\)) is the square footage, the second independent variable (\(x_2\)) is the number of bedrooms, and the third independent variable (\(x_3\)) is the age of the house. #### Effects on Selling Price of Houses | Square Feet | Number of Bedrooms | Age | Selling Price | |-------------|---------------------|-----|---------------| | 2848 | 4 | 6 | $242,100 | | 1270 | 5 | 7 | $113,600 | | 1825 | 4 | 8 | $281,700 | | 2235 | 5 | 5 | $199,100 | | 2072 | 4 | 2 | $307,500 | | 2197 | 4 | 14 | $278,800 | | 2184 | 4 | 5 | $275,300 | | 1764 | 4 | 7 | $107,200 | | 2276 | 4 | 14 | $103,000 | **Instructions:** Step 1 of 2: Find the \(p\)-value for the regression equation that fits the given data. Round your answer to four decimal places.
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