Question 1

Assume you have noted the following prices for paperback books and the number of pages that each book contains.
Develop a least-squares estimated regression line.

1. Compute the coefficient of determination and explain its meaning.
2. Compute the correlation coefficient between the price and the number of pages. Test to see if x and y are related. Use α = 0.10.

Question 2

The following data represent a company’s yearly sales volume and its advertising expenditure over a period of 8 years.

1. Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising.
2. Use the method of least squares to compute an estimated regression line between sales and advertising.
3. If the company’s advertising expenditure is $400,000, what are the predicted sales? Give the answer in dollars.
4. What does the slope of the estimated regression line indicate?

Using the ROI data set:

For each of the two majors:

1. Draw the scatter diagram of Y = ‘Annual % ROI’ against X = ‘Cost’.
2. Obtain b0 and b1 of the regression equation defined as y ̂ = b0 + b1X and the coefficient of determination (r2) from the Excel regression output.
3. Draw the fitted regression line on the scatter diagram.
4. Calculate the estimated ‘Annual % ROI’ when the ‘Cost’ (X) is $160,000.
5. Test the hypothesis:
   • H0: β1 = 0
   • Ha: β1 ≠ 0
6. Write a paragraph or more on any observations you make about the regression estimates, coefficient of determination, the plots, and the results of your hypothesis tests.