Emma is looking to purchase a home near Loyola University New Orleans. A random sample of seven homes currently listed for sale provides the following information on size (x) in hundreds of square feet, rounded to the nearest hundred, and price (y), in thousands of dollars, rounded to the nearest thousand. Construct a scatterplot of the data. What does it suggest? b. (2 points) Assuming that the simple linear regression model is appropriate, obtain the equation of the

estimated regression line. c. (2 points) What percentage of the observed variation in price can be explained by the model? d. (3 points) Check the regression assumptions using a normal probability plot of the residuals and a plot of the explanatory variable values versus the studentized residuals. [Hint: Be sure to interpret each of the plots with respect to the relevant assumption(s).] e. (3 points) Local realtors claim that there is a useful linear relationship between the two variables. Do you

agree? Carry out a formal hypothesis test to support your answer. Use a 10% significance level. f. (2 points) Give an estimate of the average change in price associated with a 100 square foot increase in size (i.e., x increases by 1 unit). Use an appropriate 90% interval. [Hint: What part of the regression equation measures the average change in Y for a one-unit increase in x?] g. (2 points) Give an estimate of the true average price for all 2000 square foot homes in this area and do so in a way that incorporates a 90% interval. [Hint 1: 2000 square feet is 20-hundred square feet. Hint 2: If done correctly, this answer will appear in the SPSS Data window.]