Determine the value of the coefficient of correlation for the following data (1/2 Point):X15829687110436Y349510301322550A 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).AdvertisingSales12.51483.75521.633860.099437.65416.18916.812641.

 

Determine the value of the coefficient of correlation for the following data (1/2 Point):

 

 

X 158 296 87 110 436   

Y 349 510 301 322 550  

 

 

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. (1 point)

 

Solve for the predicted values of y and the residuals for the data in problem 2. (1 point)

 

Determine the SSE and the standard error of the estimate (i.e., SYX) for problem 2.         (1 point)

 

 

 

 

 

 

 

 

 

 

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.            (1 point)  

 

 

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  

 

What is the coefficient of multiple determination for problem 5? (1/2 point)

 

Use the F Test to test the overall significance of the model in problem 5. (1/2 point)

 

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.    (1/2 point)

 

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.          (2 points total)

 

Assuming a linear cost relationship, what are the regression coefficients, b0 and b1?

Predict the cost per person for a restaurant with a summated rating of 50.  

What is the coefficient of determination, and what is its meaning?

What is the standard error of the estimate?

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? 

 

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.  HINT: Multiple regression.  (2 points total)

 

Write the multiple regression equation.

What are the value of the slopes, b1 and b2 in this problem?

Predict the miles per gallon for cars that have 190 horsepower and weigh 3,500 pounds.

Is there a significant relationship between mileage and the two independent variables (HP and weight) at the 0.05 level of significance?

Based on the residual plots, is there any evidence of a violation of the regression assumptions?

What is the coefficient of multiple determination?  

At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Response Sheet for HW #2 Student Name: 

 

No. Part What the question is asking for Type Your Response in this Column   

1. Coefficient of correlation r =   

 2. Regression equation   

3. Predicted values of y and the residuals  

Predicted value Residuals   

  

  

  

  

  

  

  

 

  

4. SSE and the standard error of the estimate SSE = 

SYX =   

5. The multiple regression model equation   

6. The coefficient of multiple determination r2 =   

7. Is there is evidence that at least one independent variable affects Y at  = .05?

  

8. Is there is evidence that either or both of the independent variables affect insider ownership at  = .05?   

9. a. regression coefficients, b0 and b1   

b.   

c. r2   

d. SYX   

e. “Reject the null” or “Cannot reject the null”   

10. a. The multiple regression equation   

b. Slopes, b1 and b2 b1 =

b2 =   

c. Predicted mpg when HP = 190 and weight = 3,500 pounds.   

d. “Reject the null” or “Cannot reject the null”   

e. Any evidence of a violation of the regression assumption?  Yes or no?   

f. The coefficient of multiple determination r2 =   

g. “Reject” or “Cannot reject the null” for HP?

“Reject” or “Cannot reject the null” for Weight?