# Compute the coefficient of determination and explain its meaning.

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.

- Compute the coefficient of determination and explain its meaning.
- 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.

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

Project Week 7

For these project assignments throughout the course you will need to reference the data in the ROI Excel spreadheet. Download it here.

Using the ROI data set:

For each of the two majors:

- Draw the scatter diagram of Y = ‘Annual % ROI’ against X = ‘Cost’.
- Obtain b0 and b1 of the regression equation defined as y ̂ = b0 + b1X and the coefficient of determination (r2) from the Excel regression output.
- Draw the fitted regression line on the scatter diagram.
- Calculate the estimated ‘Annual % ROI’ when the ‘Cost’ (X) is $160,000.
- Test the hypothesis:

o H0: β1 = 0

o Ha: β1 ≠ 0

- 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.