Statistics

1. A sales manager collected the following data on years of experience and annual sales (in $1000s):

                                    Years of                      Annual

Salesperson                 Experience                  Sales

1                                  1                                  80

2                                  3                                  97

3                                  4                                  92

4                                  4                                  102

5                                  6                                  103

6                                  8                                  111

7                                  10                                119

8                                  10                                123

9                                  11                                117

10                                13                                136

a. Construct a scatterplot for the data above with years of experience as the independent variable.

b. Estimate the straight-line regression equation that can be used to predict annual sales given years of experience.

c. Interpret the value of the estimated slope coefficient for years of experience.

d. Predict annual sales for a salesperson with 9 years of experience.

2. The following data are the grade-point-averages, X, and the monthly salaries, Y, for six students who received a bachelor’s degree in business administration with a major in information systems from the R.H. Smith School of Business in May 2003:

                                                Monthly

Student           GPA                Salary ($)

1                      2.6                   2800

2                      3.4                   3100

3                      3.6                   3500

4                      3.2                   3000

5                      3.5                   3400

6                      2.9                   3100

The estimated straight-line regression equation is:

Y-hat = 1290.54054 + 581.081081X

a. Calculate SSR.

b. Calculate SSE.

c. Calculate SST.

d. Calculate the coefficient of determination.

e. Interpret the value of the coefficient of determination.

f. What is the value of the sample correlation coefficient?

3. Refer to question 1. above. If SSR = 2272 and SSE = 170, use a = 0.05 and an F-test to determine whether years of experience explains a statistically significant amount of variation in annual sales (please include:  the hypotheses in words, the calculated value of the associated test statistic, the critical value of the associated test statistic, your decision, and your conclusion).

4. A manager in the commercial division of a real estate firm conducted a regression analysis to estimate the relationship between annual rents ($1000s), X, and selling

price ($1000s), Y, for apartment buildings. The following output was obtained using a statistics software program:

The regression equation is

Y = 20.0 + 7.21 X

Predictor         Coef                  StError                        t

Constant        20.000               3.2213                   6.21

X                     7.210                  1.3626                   5.29

SOURCE                  DF                   SS

Regression               1                  41587.3

Error                           7                 _______

Total                           8                  51984.1

a. How many apartment buildings were in the sample?

b. Write the estimated straight-line regression equation.

c. What is the value of the standard error for the estimated regression slope coefficient?

d. Estimate the selling price for an apartment building with annual rents of $50,000 (be careful with the units).