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Chapter 13 Exercise 6

 The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.

Car         Age (years)         Selling   Car            Age (years)        Selling Price (\$000)

Price (\$000)

1                   9                         8.1                            7                            8                              7.6

2                   7                         6.0                            8                            11                           8.0

3                  11                       3.6                            9                            10                           8.0

4                  12                       4.0                            10                         12                           6.0

5                   8                         5.0                            11                         6                              8.6

6                   7                         10.0                          12                         6                              8.0

a. If we want to estimate selling price on the basis of the age of the car, which variable is the dependent variable and which is the independent variable?

b-1. Determine the correlation coefficient. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

b-2. Determine the coefficient of determination. (Round your answer to 3 decimal places.)

c. Interpret the correlation coefficient. Does it surprise you that the correlation coefficient is negative? (Round your answer to nearest whole number.)

Chapter 13 Exercise 12

 The Student Government Association at Middle Carolina University wanted to demonstrate the relationship between the number of beers a student drinks and his or her blood alcohol content (BAC). A random sample of 18 students participated in a study in which each participating student was randomly assigned a number of 12-ounce cans of beer to drink. Thirty minutes after they consumed their assigned number of beers, a member of the local sheriff’s office measured their blood alcohol content. The sample information is reported below.

Student               Beers                    BAC                        Student                Beers                    BAC

1                              6                              0.1                          10                           3                              0.07

2                              7                              0.09                        11                           3                              0.05

3                              7                              0.09                        12                           7                              0.08

4                              4                              0.1                          13                           1                              0.04

5                              5                              0.1                          14                           4                              0.07

6                              3                              0.07                        15                           2                              0.06

7                              3                              0.1                          16                           7                              0.12

8                              6                              0.12                        17                           2                              0.05

9                              6                              0.09                        18                           1                              0.02

 Use a statistical software package to answer the following questions.

a-1. Choose a scatter diagram that best fits the data.    b. Fill in the blanks below. (Round your answers to 3 decimal places.)

c. Determine the coefficient of correlation and coefficient of determination. (Round your answers to 3 decimal places.)

c-1.  State the decision rule for .01 significance level: H0: ρ ≤ 0; H1: ρ > 0. (Round your answer to 3 decimal places.)

c-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

c-3. What is the p-value? (Hint: use your analysis software) (Round p-value to 4 decimal places.)

c-4.  At the .01 significance level, is it reasonable to conclude that there is a positive relationship in the population between the number of beers consumed and the BAC?

Chapter 13 Exercise 14

 The following sample observations were randomly selected.   a. Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

b. Determine the value of when X is 7. (Round your answer to 3 decimal places.)

Chapter 13 Exercise 22

 The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.

Car        Age (years)    Selling Price (\$000)               Car         Age (years)         Selling Price (\$000)

1                              9                              8.1                          7                             8                              7.6

2                              7                              6                              8                             11                           8

3                              11                           3.6                          9                             10                           8

4                              12                           4                              10                           12                           6

5                              8                              5                              11                           6                              8.6

6                              7                              10                           12                           6                              8

The regression equation is, the sample size is 12, and the standard error of the slope is 0.23. Use the .05 significance level. Can we conclude that the slope of the regression line is less than zero?

Chapter 13 Exercise 26

 The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.

Car         Age (years)         Selling Price (\$000)

1                              9                              8.1

2                              7                              6.0

3                              11                           3.6

4                              12                           4.0

5                              8                              5.0

6                              7                              10.0

7                              8                              7.6

8                              11                           8.0

9                              10                           8.0

10                           12                           6.0

11                           6                              8.6

12                           6                              8.0

a. Determine the standard error of estimate. (Round your answer to 3 decimal places.)

b. Determine the coefficient of determination. (Round your answer to 3 decimal places.)

c. Interpret the coefficient of determination. (Round your answer to the nearest whole number.)

Chapter 14 Exercise 2

Thompson Photo Works purchased several new, highly sophisticated processing machines. The production department needed some guidance with respect to qualifications needed by an operator. Is age a factor? Is the length of service as an operator (in years) important? In order to explore further the factors needed to estimate performance on the new processing machines, four variables were listed:

X1 = Length of time an employee was in the industry

X2 = Mechanical aptitude test score

X3 = Prior on-the-job rating

X4 = Age

Performance on the new machine is designated y.

 Thirty employees were selected at random. Data were collected for each, and their performances on the new machines were recorded. A few results are:

Performance                     Length of                             Mechanical                         Prior

on New                                                Time in                                 Aptitude                              On-the-Job

Machine,                             Industry,                              Score,                                   Performance,                    Age,

Name                                    Y                                  X1                                          X2                                        X3                                             X4

Mike Miraglia                     112                             12                                          312                                      121                                         52

Sue Trythall                        113                              2                                         380                                         123                                         27

 The equation is:

Ŷ = 11.6 + 0.4X1 + 0.286X2 + 0.112X3 + 0.002X4

a. What is this equation called?

b. How many dependent and independent variables are there?

c. What is the number 0.286 called?

d. As age increases by one year, how much does estimated performance on the new machine increase? (Round your answer to 3 decimal places.)

e. Carl Knox applied for a job at Photo Works. He has been in the business for 6 years and scored 280 on the mechanical aptitude test. Carl’s prior on-the-job performance rating is 97, and he is 35 years old. Estimate Carl’s performance on the new machine. (Round your answer to 3 decimal places.)

Chapter 14 Exercise 6

 Consider the ANOVA table that follows.

Analysis of Variance Source                                         DF                           SS                           MS                         F

Regression                                                                          5                              3710                       742                         12.89

Residual Error                                                                    46                           2647.38 57.55

Total                                                                                      51                           6357.38

a-1. Determine the standard error of estimate. (Round your answer to 2 decimal places.)

a-2. About 95% of the residuals will be between what two values? (Round your answers to 2 decimal places.)

b-1. Determine the coefficient of multiple determination. (Round your answer to 3 decimal places.)

c. Determine the coefficient of multiple determination, adjusted for the degrees of freedom. (Round your answer to 3 decimal places.)

Chapter 14 Exercise 8

 The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars.

Predictor            Co eff                    SE Co eff              t                              p-value

Constant              7.987                     2.967                     2.69                        0.01

X1                           0.122                     0.031                     3.92                        0

X2                           –1.120                   0.053                     –2.270                   0.028

X3                           –0.063                   0.039                     –1.610                   0.114

X4                           0.523                     0.142                     3.69                        0.001

X5                           –0.065                   0.04                        –1.620                   0.112

Analysis of Variance

Source                                  DF                           SS                           MS                         F                              p-value

Regression                          5                              3710                       742                         12.89                     0

Residual Error                    46                           2647.38 57.55

Total                                     51                           6357.38

X1 is the number of architects employed by the company.

X2 is the number of engineers employed by the company.

X3 is the number of years involved with health care projects.

X4 is the number of states in which the firm operates.

X5 is the percent of the firm’s work that is health care–related.

a. Write out the regression equation. (Round your answers to 3 decimal places. Negative answers should be indicated by a minus sign.)

b. How large is the sample? How many independent variables are there?

c-1. State the decision rule for .05 significance level: H0: β1 = β2 = β3 =β4 =β5 =0; H1: Not all β's are 0. (Round your answer to 2 decimal places.)

c-2. Compute the value of the F statistic. (Round your answer to 2 decimal places.)

c-3. Can we conclude that the set of regression coefficients could be different from 0? Use the .05 significance level.

d-1. State the decision rule for .05 significance level. (Round your answers to 3 decimal places.)

d-2. Compute the value of the test statistic. (Round your answers to 2 decimal places. Negative answers should be indicated by a minus sign.)

d-3. Which variable would you consider eliminating?