Marvin is a safety inspector at a large industrial plant that has eight division
ID: 3152830 • Letter: M
Question
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.
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
numbers above are s=14.0233
r-sq=68.0%
r-sq(adj)=62.6%
1. (Cont’d)
a. State the direction of the relationship between the two variables and interpret its meaning in the context of this problem.
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.
c. 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.
d. 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.
e. 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?
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
Fitted Line Plot Hours Lost81.92-1.233 Safety Training 2 4033 CHI R-Sq 70 G 40 E 10 20 30 40 50 Number of worle hours in safety trainingExplanation / Answer
a. Relationship between the 2 variables: number of work-hours devoted to safety training and the number of work-hours lost due to industry-related accidents has a negative direction as these variables are negatively related.
Interpretation: As safety training work-hours increase, the work hours lost due to accidents decrease.
b. Regression on this model is significant as the p-value of pearson correlation coefficient is less than 0.05. So use of regression to get a line of best fit is appropriate, however, a high number of data points would have given a more accurate estimate.
c. If 35 hours are spent on safety training, using line of best fit:
Hours lost = 81.92 - 1.233*Safety training,
Hours lost = 81.92 - 1.233*35 = 38.765
So, only 38.765 hours will be lost if 25 hours are spent on safety training.
d. Using line of best fit,
Hours lost = 81.92 - 1.233*52 = 17.804 hours
As he estimated 20 hours, error = 2.196 hours
This is much less tha Standard error (S) = 14.0233 hours
So it is a reasonable estimate.
e. Using line of best fit,
Hours lost = 81.92 - 1.233*25 = 51.095 hours
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