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What are the degrees of freedom in the overall f test

**Problem**

Zach has collected the data of several Stanley Cup rings sold in the Hockey Memorabilia auctions in the past year and plans to use the data to predict the average selling prices of similar items in the upcoming auction. The data includes final auction selling price, weight, and type of metal (10K Gold, 14K Gold or Sterling Silver), as well as whether each ring had diamonds or not.

1. Help Zach to construct a multiple regression model for this problem. (Hint: Create a set of binary independent variables to represent the metal types, and another independent variable for the diamond). Provide the mathematical equation of the regression model, and then perform the regression analysis in Excel.

2. What is the estimated regression function?

3. Interpret the value of R2 for this model.

4. Write down the hypothesis test for the overall significance of this model (write the null and alternative hypotheses). What are the degrees of freedom in the overall F test?

5. What is p-value of the overall F test? (Hint: use Excel's regression report). Assuming α = 0.05, How would you use p-value to decide whether to reject the null hypothesis or not?

6. What other variables do you think Zach could consider including in the model to help improve the model?

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