1. Determine the value of the coefficient of correlation for the following data:
|
X
|
158
|
296
|
87
|
110
|
436
|
|
Y
|
349
|
510
|
301
|
322
|
550
|
2. A corporation owns several companies. The strategic planner for the corporation believes dollars spent on advertising can to some extent be a predictor of total sales dollars. As an aid in long-term planning, she gathers the following sales and advertising information from several of the companies ($ millions).
|
Advertising
|
Sales
|
|
12.5
|
148
|
|
3.7
|
55
|
|
21.6
|
338
|
|
60.0
|
994
|
|
37.6
|
541
|
|
6.1
|
89
|
|
16.8
|
126
|
|
41.2
|
379
|
Develop the equation of the simple regression line to predict sales from advertising expenditures using these data.
3. Solve for the predicted values of y and the residuals for the data in problem 2.
4. Determine the SSE and the standard error of the estimate (i.e., SYX) for problem 2.
5. Jenson, Solberg, and Zorn investigated the relationship of insider ownership debt, and dividend policies in companies. One of their findings was that firms with high insider ownership choose levels of debt and dividends. Shown here is a sample of data of these three variables for 11 different industries. Use the data to develop the equation of the regression model to predict insider ownership by debt ratio and dividend payout.
|
Industry
|
Insider Ownership
|
Debt Ratio
|
Dividend Payout
|
|
Mining
|
8.2
|
14.2
|
10.4
|
|
Food & Beverage
|
18.4
|
20.8
|
14.3
|
|
Furniture
|
11.8
|
18.6
|
12.1
|
|
Publishing
|
28.0
|
18.5
|
11.8
|
|
Petroleum Refining
|
7.4
|
28.2
|
10.6
|
|
Glass & Cement
|
15.4
|
24.7
|
12.6
|
|
Motor Vehicle
|
15.7
|
15.6
|
12.6
|
|
Department Store
|
18.4
|
21.7
|
7.2
|
|
Restaurant
|
13.4
|
23.0
|
11.3
|
|
Amusement
|
18.1
|
46.7
|
4.1
|
|
Hospital
|
10.0
|
35.8
|
9.0
|
6. What is the coefficient of multiple determination for problem 5?
7. Use the F Test to test the overall significance of the model in problem 5.
8. Are individual variables significant in problem 5? Use the t Test to check for the effect of the individual variables, Debt Ratio and Dividend Payout, on Insider Ownership.
9. Zagat's publishes restaurant ratings for various locations in the U.S. The Excel file Restaurants contains the Zagat rating for food, décor, service, and the cost per person for a sample of 100 restaurants located in NYC and in a suburb of NYC. Develop a regression model to predict the price per person, based on a variable that represents the sum of the ratings for food, décor, and service. HINT: Simple Linear Regression.
a. Assuming a linear cost relationship, what are the regression coefficients, b0 and b1?
b. Predict the cost per person for a restaurant with a summated rating of 50.
c. What is the coefficient of determination, and what is its meaning?
d. What is the standard error of the estimate?
e. Using the t Test for the correlation coefficient is there evidence of a significant association between the price per person and a restaurants summated rating?
10. How does horsepower and weight affect the mileage of family sedans? Data from a sample of twenty 2010 family sedans were collected and organized and stored in the Excel file Auto2010. Develop a regression model to predict mileage (as measured by miles per gallon) based on the horsepower of the car's engine and the weight of the car, in pounds.
a. Write the multiple regression equation.
b. What are the value of the slopes, b1 and b2 in this problem?
c. Predict the miles per gallon for cars that have 190 horsepower and weigh 3,500 pounds.
d. Is there a significant relationship between mileage and the two independent variables (HP and weight) at the 0.05 level of significance?
e. Based on the residual plots, is there any evidence of a violation of the regression assumptions?
f. What is the coefficient of multiple determination?
g. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model.