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- From: Mathematics, Statistics and Probability
- Posted on: Sat 23 Jan, 2016
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16.100
Xr16-100 The president of a company that manufactures car seats has been concerned about the number and cost of machine breakdowns. The problem is that the machines are old and becoming quite unreliable. However, the cost of replacing them is quite high, and the president is not certain that the cost can be made up in today’s slow economy. To help make a decision about replacement, he gathered data about last month’s costs for repairs and the ages (in months) of the plant’s 20 welding machines.
• a. Find the sample regression line.
• b. Interpret the coefficients.
• c. Determine the coefficient of determination, and discuss what this statistic tells you.
• d. Conduct a test to determine whether the age of a machine and its monthly cost of repair are linearly related.
• e. Is the fit of the simple linear model good enough to allow the president to predict the monthly repair cost of a welding machine that is 120 months old? If so, find a 95% prediction interval. If not, explain why not.
Age Repairs
110 327.67
113 376.68
114 392.52
134 443.14
93 342.62
141 476.16
115 324.74
115 338.98
115 433.45
142 526.37
96 362.42
139 448.76
89 335.27
93 350.94
91 291.81
109 467.8
138 474.48
83 354.15
100 420.11
137 416.04
17.2 - Pat Statsdud, a student ranking near the bottom of the statistics class, decided that a certain amount of studying could actually improve final grades. However, too much studying would not be warranted, since Pat's ambition (if that's what one could call it) was to ultimately graduate with absolute minimum level of work. Pat was registered in a statistics course, which had only 3 weeks to go before the final exam, and where the final grade was determine in the following way:
Total mark = 20% (assignment)
+ 30% (midterm)
+ 50% (final exam)
To determine how much work to do in the remaining 3 weeks, Pat needed to be able to predict the final exam mark on the basis of the assignment mark (worth 20 points) and the midterm mark (worth 30 points). Pat's marks on these were 12/20 and 14/30, respectively. Accordingly, Pat undertook the following analysis. The final exam mark, assignment mark, and midterm test mark for 30 students who took the statistics course last year were collected.
Final (y) Assignment (x1) Midterm (x2)
23 15 11
49 15 28
34 13 19
43 20 26
43 20 22
29 18 13
31 20 10
30 10 11
36 13 16
33 16 15
39 19 16
33 20 16
24 10 12
36 12 22
29 10 13
43 15 23
50 12 28
40 14 20
42 11 20
35 13 15
31 15 10
48 19 30
42 13 16
37 13 24
40 18 20
30 10 16
25 20 10
33 11 18
30 12 13
25 14 15
A) Determine the regression equation.
B) What is the standard error of estimate?
C) What is the coefficient of determination? What does this statistic tell you?
D) Test the validity of the model.
E) Interpret each of the coefficients.
F) Can Pat infer that the assignment mark is linearly related to the final grade in this model?
G) Can Pat Infer that the midterm mark is linearly related to the final grade in this model?
H) Predict Pat’s final exam mark with 95% confidence.
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