Question

1. A random sample of nine custom homes currently listed for sale provided the following information on size and price. Here, x denotes size, in hundreds of square feet, rounded to the nearest hundred, and y denotes price, in thousands of dollars, rounded to the nearest thousand.

The summaries of the data are given by

n=9, ∑xi=270, ∑x2i=8316, ∑yi=5552, ∑y2i=3504412, ∑xiyi=169993

1. Given the summaries of the data, find the least-squares regression equation.

2. Graph the regression equation and the data points.

3. Interpret the slope of the regression equation obtained in part (a) in the context of the study.

4. Calculate

   r

   , the correlation coefficient between

   y

   and

   x

   . Interpret the number.

5. Calculate the coefficient of determination

   r2

   . Interpret the number.

6. Test at the 5% significant level, whether the size is a useful predictor for the price of the custom homes. You could use

   se=59.62

   .

7. Obtain a 95% confidence interval for the slope of the population regression line that relates price to size for custom homes.

8. Interpret the confidence interval obtained in part (g). Does this interval support the results of the hypothesis test in part (f). (4 marks: 2+2)

Answer 1