MAT 121 Assignment Problems

1. Marvin is a safety inspector at a large industrial plant that has eight divisions that do the same type of work. He recorded the number of work-hours devoted to safety training and the number of work-hours lost due to industry-related accidents for each of the divisions last quarter. This data is in the table below.

Number of work-hours in safety training

9

21

27

42

50

55

41

35


Number of work-hours lost due to accidents

73

45

68

35

35

10

12

32




Marvin used this data to predict the number of work-hours lost due to accidents based upon the number of work-hours spent in safety training using linear regression analysis. His Minitab output is given below. (50 points)





Marvin’s Minitab output:



Correlations: No. of Hours Safety Training, No. of Hours Lost Accidents



Pearson correlation of No. of Hours Safety Training and No. of Hours Lost Accidents = - 0.824

P-Value = 0.012


Scatterplot (rtf file)
Scatterplot (mpj file)
















1. (Cont’d)

a. State the direction of the relationship between the two variables and interpret its meaning in the context of this problem.(8 points)



b. Explain whether or not Marvin’s use of regression analysis to produce the equation of the "line of best fit" was appropriate in this situation. (8 points)



c. Label two points (ordered pairs) that fall on the "line of best fit" on the scatterplot. Show your work. (8 points)



d. What would Marvin predict to be the number of work-hours lost due to accidents if 35 hours are spent on safety training? Show how you arrived at your answer and interpret its meaning in the context of this problem. (10 points)



e. Marvin’s supervisor guessed that if 52 hours were spent on safety training then the number of work-hours lost due to accidents would be 20 hours. Explain whether or not this guess was reasonable. (8 points)



f. Marvin’s brother Michael supervises cashiers at Wegmans Supermarkets. What should Michael predict to be the number of work-hours lost by a cashier at Wegmans due to accidents when that cashier has had 25 hours of safety training? (8 points)





2. The following correlation coefficients, (r values), and P-values were generated with Minitab.

Each of the columns X1, X2, X3, X4, Y1, Y2, Y3, and Y4 have the same number of data items in them.

Correlation of X1 and Y1 = - 0.998, P-value = 0.000

Correlation of X2 and Y2 = 0.471, P-value = 0.169

Correlation of X3 and Y3 = 0.856, P-value = 0.002

Correlation of X4 and Y4 = - 0.662, P-value = 0.037

Use this information to answer each question that follows. (30 points)

a. The strongest association is between which pair of variables?

Underline one: (6 points)



i. X1 and Y1 ii. X2 and Y2 iii. X3 and Y3 iv. X4 and Y4



b. The weakest correlation exists between which pair of variables?

Underline one: (6 points)
i. X1 and Y1 ii. X2 and Y2 iii. X3 and Y3 iv. X4 and Y4



c. The relationship between X3 and Y3 is _________?

Underline one: (6 points)

i. positve ii. negative



d. There is a stronger correlation between X4 and Y4 than between X3 and Y3?

Underline one: (6 points)

i. true ii. false



e. For which pair would it not be appropriate to perform regression analysis to produce the equation of the "line of best fit" for the relationship, as indicated by the P-value?

Underline one: (6 points)

i. X1 and Y1 ii. X2 and Y2 iii. X3 and Y3 iv. X4 and Y4



DIRECTIONS: Show your work or explain how you arrived at your conclusion whenever appropriate.


80 points





1. Marvin is a safety inspector at a large industrial plant that has eight divisions that do the same type of work. He recorded the number of work-hours devoted to safety training and the number of work-hours lost due to industry-related accidents for each of the divisions last quarter. This data is in the table below.




Number of work-hours in safety training

9

21

27

42

50

55

41

35


Number of work-hours lost due to accidents

73

45

68

35

35

10

12

32




Marvin used this data to predict the number of work-hours lost due to accidents based upon the number of work-hours spent in safety training using linear regression analysis. His Minitab output is given below. (50 points)


Marvin’s Minitab output:


Correlations: No. of Hours Safety Training, No. of Hours Lost Accidents


Pearson correlation of No. of Hours Safety Training and No. of Hours Lost Accidents = - 0.824

P-Value = 0.012


Scatterplot (rtf file)
Scatterplot (mpj file)

1. (Cont’d)

a. State the direction of the relationship between the two variables and interpret its meaning in the context of this problem.(8 points)



b. Explain whether or not Marvin’s use of regression analysis to produce the equation of the "line of best fit" was appropriate in this situation. (8 points)



c. Label two points (ordered pairs) that fall on the "line of best fit" on the scatterplot. Show your work. (8 points)



d. What would Marvin predict to be the number of work-hours lost due to accidents if 35 hours are spent on safety training? Show how you arrived at your answer and interpret its meaning in the context of this problem. (10 points)



e. Marvin’s supervisor guessed that if 52 hours were spent on safety training then the number of work-hours lost due to accidents would be 20 hours. Explain whether or not this guess was reasonable. (8 points)



f. Marvin’s brother Michael supervises cashiers at Wegmans Supermarkets. What should Michael predict to be the number of work-hours lost by a cashier at Wegmans due to accidents when that cashier has had 25 hours of safety training? (8 points)





2. The following correlation coefficients, (r values), and P-values were generated with Minitab.

Each of the columns X1, X2, X3, X4, Y1, Y2, Y3, and Y4 have the same number of data items in them.

Correlation of X1 and Y1 = - 0.998, P-value = 0.000

Correlation of X2 and Y2 = 0.471, P-value = 0.169

Correlation of X3 and Y3 = 0.856, P-value = 0.002

Correlation of X4 and Y4 = - 0.662, P-value = 0.037

Use this information to answer each question that follows. (30 points)


a. The strongest association is between which pair of variables?

Underline one: (6 points)



i. X1 and Y1 ii. X2 and Y2 iii. X3 and Y3 iv. X4 and Y4



b. The weakest correlation exists between which pair of variables?

Underline one: (6 points)
i. X1 and Y1 ii. X2 and Y2 iii. X3 and Y3 iv. X4 and Y4



c. The relationship between X3 and Y3 is _________?

Underline one: (6 points)

i. positve ii. negative



d. There is a stronger correlation between X4 and Y4 than between X3 and Y3?

Underline one: (6 points)

i. true ii. false



e. For which pair would it not be appropriate to perform regression analysis to produce the equation of the "line of best fit" for the relationship, as indicated by the P-value?

Underline one: (6 points)

i. X1 and Y1 ii. X2 and Y2 iii. X3 and Y3 iv. X4 and Y4