correlation analysis and the regression statistics

1).  When you take out a mortgage, there are many different kinds of costs.  Usually the two largest are the interest rate (annual percentage that determines the size of your monthly payment) and the loan fee (a one-time percentage charged to you at the time the loan is made).  Based on the data in the MORTAGE tab of the Excel file provided, what type of relationship exists between the interest rate and loan fee?  How strong of a relationship exists between these two variables?  If one wanted to predict the loan fee given a certain interest rate, would you recommend using a model derived from this data?  Only use correlation analysis and the regression statistics to briefly justify your reasoning.  Use α = .05.

2).  The data in the MATH tab of the Excel file provided represents a sample of mathematics achievement test (MAT) scores and calculus grades for independently selected college freshmen.  From this evidence, would you say that the achievement test scores and calculus grades are independent?

Use α = .01.

3).  Part of a study to determine factors influencing family medical expenses involves finding a regression relationship between the number of people in a family and the monthly medical expense.  The data for the pilot study is located in the MEDICAL tab in the Excel file provided.

a).  Develop a regression model at the .05 level of significance.

b).  What can be said regarding the slope and correlation coefficient?  Conduct both the (t)-test and F-test for the slope, and (t)-test for the correlation coefficient.

c).  Use your results in (a) to determine the monthly medical expenses for a family of (4)?  Is this meaningful?

d).  Use your results in (a) to determine the monthly medical expenses for single person household?  Is this meaningful?

4).  Consider the earnings per share and the closing stock price of selected biotechnical firms with large market capitalization located in the STOCK tab in the Excel file provided.  Given the importance of many analysts place on earnings per share, you might expect to find a strong correlation between earnings per share and stock price.  Of course, it may be premature to judge since the market price may depend more on the expectation of (random) future earnings than on the actual achieved earnings.  (20 pts)

a).  Draw a scatterplot of the stock price against earnings per share.

b).  Determine the coefficient of determination and interpret its meaning.

c).  Using α = .05, develop a regression model.

d).  Conduct a residual analysis and determine the validity of the model.  Include the Durbin-Watson test.

e).  You are head of a biotech firm planning to go public soon.  Your earnings per share are \$.05.  Based on your model in (c), what stock price would you anticipate.

5).  A sample of 30 computer hardware companies were observed from Stock Investor Pro and is located in the INVESTOR tab in the Excel file provided.  The data includes price per share, book value per share, and the return on equity per share for each.

a).  Develop an estimated regression model that can be used to predict the price per share given the book value per share and the return on equity per share.  Use the .05 level of significance.

b).  Test the significance of the overall regression model.

c).  Use the (t)-test and partial F-test to determine the significance of each independent variable.

d).  Do the independent variables make a significant contribution to the regression model?  Which one(s) should be included?

e).  Compute the coefficients of partial determination and interpret the results.

f).  Add an interaction term to the model.  Does it make a significant contribution to the model?

6).  Your firm is worried about being sued for gender discrimination.  There is a growing perception that males are being paid more than females in your department.  Using the data in the SALARY tab in the Excel file provided, please complete the following using α = .05:

a).  Do the men appear to earn more on average than women based on the information provided?

b).  Derive a regression model, and provide a model for men and a model for women.

c).  Do the independent variables make a significant contribution to the regression model?  Which one(s) should be included?

d).  Compute the coefficients of partial determination and interpret the results.

e).  Add an interaction term to the model.  Does it make a significant contribution to the model?

f).  How does the salary differ for men and women if each one has 13-years experience?

g).  Does your results imply discrimination against women?

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