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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. Go to Excel. Create a scatter diagram for the data. Include the trendline (regression line). Make sure from Week 1 you know what a trendline is. It is NOT simply connecting the dots.
  2. Once the scatter diagram is created, right-click on the trendline itself in the graph. Use the “format trendline” from the menu to show the equation of the trendline and the r squared value on the graph itself.
  3. Provide the coefficient of determination and explain its meaning.
  4. Provide the correlation coefficient between the price and the number of pages.
  5. Run the regression analysis as demonstrated in the video lecture. Follow the directions of what to analyze to test and see if x and y are related. Use α = 0.10.
    1. What is your null and alternative hypotheses?
    2. What is the t value?
    3. What are the degrees of freedom?
    4. On what basis do you reject of fail to reject the null hypothesis?

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. Make sure your axes are labeled and that you have the axes correct (notice that x and y are above the labels). The graph should have a title that mentions the two variables.
  2. Use the method of least squares to compute an estimated regression line between sales and advertising OR just show it on the graph along with your r-squared value..
  3. If the company’s advertising expenditure is $200,000, what are the predicted sales? Give the answer in dollars. (This is found using algebra and the equation of the trendline / regression line – make sure to watch your units)
  4. What does the slope of the estimated regression line indicate?

Question 3

For this question you will need to reference the data in the ROI Excel spreadsheet. Download it here.

Using the ROI data set:

For each of the two majors:

  1. Draw the scatter diagram of Y = ‘Annual % ROI’ against X = ‘Cost’. Include the trendline (regression line) and the r-squared value (coefficient of determination).
  2. Obtain b0 and b1 of the regression equation defined as y ̂ = b0 + b1X (y intercept and slope).
  3. Calculate the estimated ‘Annual % ROI’ when the ‘Cost’ (X) is $160,000. (algebra using the equation of the line)
    • H0: β1 = 0
    • Ha: β1 ≠ 0
    • In a highlighted box, 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. Please note the plural nature – paragraph or MORE, hypothesis tests – there is a focus on the comprehensive nature of this final part of the project. One way to set this part of the project up is to first talk about each test – what is it, what does it test for? Then show your work and discuss the outcome. Repeat this for each test. Summarize findings at the end.

Test the hypothesis: You will need to show work for the tests you are performing – t-tests, F tests…see the end of chapter 12 to make sure you are doing a comprehensive analysis.

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