To find the p-value for the regression equation that fits the given data, we'll need to conduct a multiple regression analysis with the following dataTo find the p-value for the regression equation that fits the given data, we'll need to conduct a multiple regression analysis with the following

• Dependent variable (Y): Selling Price
• Independent variables:
  • $x_1$: Square Feet
  • $x_2$: Number of Bedrooms
  • $x_3$: Age of the House

The p-value in a regression analysis typically tells us whether the overall regression model is statistically significant, i.e., if there's at least one predictor (independent variable) that has a significant effect on the dependent variable (selling price).

Here’s how we proceed with finding the p-value:

1. Prepare the Data: Organize the data into a format suitable for regression analysis.
2. Run a Multiple Regression: Using statistical software or a calculator, input the data to calculate the regression model.
3. Interpret the p-value: The p-value associated with the F-statistic in the regression output will tell us if the regression model is significant.

Given that I can’t directly compute this without running statistical software here, I’ll outline the steps for calculating it with software like Python or Excel, or if you have access to a calculator that performs regression analysis:

Step-by-Step Guide for Finding the p-value

1. Input the Data: Enter the data into the software:

   • Square Feet: [3097, 2726, 2686, 2391, 2357, 2207, 1914, 1666, 1146]
   • Number of Bedrooms: [5, 5, 5, 4, 4, 3, 3, 3, 3]
   • Age: [14, 13, 13, 12, 12, 11, 11, 7, 4]
   • Selling Price: [287800, 278300, 222300, 174700, 160900, 158600, 152000, 130300, 116500]

2. Run the Regression: Select multiple regression analysis in the software, setting the dependent variable as Selling Price and the independent variables as Square Feet, Number of Bedrooms, and Age.

3. Locate the p-value: After running the regression, look at the regression output for the p-value associated with the F-statistic. This p-value tests the null hypothesis that all regression coefficients are equal to zero (no effect).

4. Interpret: A p-value less than a significance level (commonly 0.05) would suggest that at least one of the independent variables significantly affects the selling price.

If you’d like, I can help interpret the output if you provide it, or guide you through using a specific tool for regression analysis. Let me know how you'd like to proceed!

Would you like details on using software for this calculation?

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Related Questions:

1. How do we interpret individual coefficients in a multiple regression model?
2. What does the p-value of each independent variable indicate?
3. How do we determine which independent variable has the most influence on the dependent variable?
4. What is multicollinearity, and how could it affect this regression model?
5. How does adjusting the model affect the overall p-value?

Tip: In multiple regression analysis, check the $R^2$ value to understand the proportion of variance explained by the model, and the individual p-values to see which predictors are significant.