# Thompson Photo Works purchased several new, highly sophisticated machines

January 30, 2017

Question
Complete the following textbook exercises:

2, 4, 6, 14 and 22 a,b,c,d

2. Thompson Photo Works purchased several new, highly sophisticated 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 a machine operator important? In order to explore further the factors needed to estimate performance on the new machines, four variables were listed:

X1= Length of time employee was a machinist. (LOTM)

X2 = Machanical aptitude test score. (MAS)

X3 = Prior on-the-job rating. (OTJT)

X4 = Age.

Performance on the new machine is designated Y.

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

Name Performance LOTM MAS OTJP Age

Andy Kosin 112 12 312 121 52

Sue Annis 113 2 380 123 27

The equation is:

.0/msohtmlclip1/01/clip_image002.png”>Y1 (upper) = 11.6 + 0.4X1 + 0.286X2 + 0.112X3+ 0.002X4

a. What is the equation called?

b. How many dependent variables are there? Independent variables?

c. What is the number 0.286 called?

d. As age increases by one year, how much does estimated performance on the new machines increase?

e. Carl Knox applied for the job at Photo Works. He has been a machinist for six years, and scored 280 on the MAS. Carl’s prior on-the-job performance rating is 97, and he is 35 years old. Estimate Carl’s performance on the new machine.

4.Cellulon, a manufacturer of a new type of home insulation, wants to develop guidelines for builders and consumers regarding the effects on natural gas consumption (1) of the thickness of the insulation in the attic of a home and (2) of the outdoor temperature. In the laboratory they varied the insulation thickness and temperature. A few of the findings are:

Mo. Nat. Gas Thickness of Outdoor

Consumption Insulation Temperature

(cubic ft) (cm) (Celsius)

Y X1 X2

30.3 12.5 4

26.9 30 4

22.1 20 9

Based on the sample results, the regression equation is:

.0/msohtmlclip1/01/clip_image002.png”>Y1 (upper) = 38.12 – 0.194X1 – 1.349X2

a. How much natural gas can homeowners expect to use per month if they install 15cm of insulation and the outdoor temperature is 10 degrees Celsius.

b. What effect would installing 18cm of insulation instead of 15 have on the monthly natural gas consumption (assuming the outdoor temperature remains at 10 degrees Celsius)?

c. Why are the regression coefficients, b1 and b2, negative? Is this logical?

6. Refer to the following ANOVA table.

Source DF SS MS F

Regression 5 3710.0 742.00 12.89

Error 46 2647.38 7

Total 51 6357.38

a. How large was the sample?

b. How many independent variables are there?

c. How many dependent variables are there?

d. Compute the standard error of estimate. About 95% of the residuals will be between what two values?

e. Determine the coefficient of multiple determination. Interpret this value.

14. In a multiple regression equation two independent variables are considered, and the sample size is 25. The regression coefficients and the standard errors are as follows.

B1= 2.676 Sb1 = 0.56

B2 = -0.880 Sb2 = 0.71

Conduct a test of hypothesis to determine whether either independent variable has a coefficient equal to zero. Would you consider deleting either variable from the regression equation? Use the .05 significance level.

22. Fran’s Convenience Marts are located throughout a metropolitan area. Fran, the owner, would like to expand into other communities. As part of her presentation to the local bank, she would like to better understand the factors that make a particular outlet profitable. She must do all the work herself, so she will not be able to study all her outlets. She selects a random sample of 15 marts and records the average daily sales (Y), the floor space (areas), the number of parking spots, and the median income of families in each region. The sample information is reported below:

Sampled Daily Store Parking Income

Mart Sales (\$) Area Spaces (\$ thousands)

1 \$1840 532 6 \$44

2 1746 478 4 51

3 1812 530 7 45

4 1806 508 7 46

5 1792 514 5 44

6 1825 556 6 46

7 1811 541 4 49

8 1803 513 6 52

9 1830 532 5 46

10 1827 537 5 46

11 1764 499 3 48

12 1825 510 8 47

13 1763 490 4 48

14 1846 516 8 45

15 1815 482 7 43

a. Determine the regression equation.

b. What is the value of R? Comment on the value.

c. Conduct a global hypothesis test to determine if any of the independent variables are different from zero. Test at a significance level of .05.

d. Conduct individual hypothesis tests to determine if any of the independent variables can be dropped. Test at a significance level of .05.

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