Question: Random sample of nine custom homes listed for sale provided following information on size & price. Here, x denotes size, in hundreds of square feet, rounded to nearest hundred, and y denotes price, in thousands of dollars, rounded to nearest thousand.

X 26 27 33 29 29 34 30 40 22

Y 290 305 325 327 356 411 488 554 246

1. Determine the regression equation for the data.
2. Graph the regression equation and the data points.
3. Describe the apparent relationship between square footage and price for custom homes.
4. What does the slope of the regression line represent in terms of size and price of custom homes?
5. Use the regression equation determined in part (a) to predict the price of a custom home that has 2600 square feet?
6. Identify the predictor and response variables.
7. Identify the outliers and potential influential observations.
8. Obtain the linear correlation coefficient by using the computing formula
9. Interpret the value of r in terms of the linear relationship between the two variables in question.
10. Discuss the graphical interpretation of the value of r and verify that it is consistent with the graph you obtained earlier in this exercise.
11. Square r and compare the result with the value of the coefficient of determination obtained earlier in this exercise.
12. In problem L, we repeat the information from A through G. For each exercise, discuss what satisfying assumptions 1 – 3 for regression inferences by the variables under consideration would mean.
13. Compute the standard error of the estimate and interpret your answer.
14. Interpret your result from part M if the assumptions for regression inferences hold.
15. Obtain a residual plot and a normal probability plot of the residuals.
16. Decide whether you can reasonably consider assumptions 1 – 3 for regression inferences to be met by the variables under consideration. (The answer here is subjective, especially in view of the extremely small sample size).
17. In problem Q, we repeat information from P. Presuming that the assumptions for regression inferences are met, perform the required hypothesis tests, using either the critical-value approach or the P-value approach. (Recall that you previously obtained the sample regression equations in A-G and the standard errors of the stimate in M-P.
18. Find a 99% confidence interval for the slope of the population regression linethat relates price to size for custom homes and interpret your answer
19. Determine a point estimate for the mean price of all 2800 square foot homes.
20. Find a 99% confidence interval for the mean price of a 2800 square foot home.
21. Find the predicted price of a 2800 suare foot home.
22. Determine a 99% prediction interval for the price of a 2800 square foot home.
23. At the 0.5% significance level, do the data provide sufficient evidence to conclude that, for custom homes, size and price are positively linearly correlated?

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