(TCO E) The Central Company manufactures a certain item once a week in a batch production run. The number of items produced in each run varies from week to week as demand fluctuates. The company is interested in the relationship between the size of the production run (SIZE, X) and the number of personhours of labor (LABOR, Y). A random sample of 13 production runs is selected, yielding the data below.
SIZE 
LABOR 
PREDICT 
40 
83 
60 
30 
60 
100 
70 
138 

90 
180 

50 
97 

60 
118 

70 
140 

40 
75 

80 
159 

70 
140 

40 
75 

80 
159 

70 
144 

50 
90 

60 
125 

50 
87 

Correlations: SIZE, LABOR
Pearson correlation of SIZE and LABOR = 0.990
PValue = 0.000
Regression Analysis: EMP. versus FLIGHTS
The regression equation is
LABOR = – 6.16 + 2.07 SIZE
Predictor Coef SE Coef T P
Constant 6.155 5.297 1.16 0.270
SIZE 2.07371 0.08717 23.79 0.000
S = 5.20753 RSq = 98.1% RSq(adj) = 97.9%
Analysis of Variance
Source DF SS MS F P
Regression 1 15349 15349 565.99 0.000
Residual Error 11 298 27
Total 12 15647
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 118.27 1.45 (115.07, 121.46) (106.37, 130.17)
2 201.22 3.90 (192.64, 209.80) (186.90, 215.53)X
X denotes a point that is an extreme outlier in the predictors.
Values of Predictors for New Observations
New Obs SIZE
1 60
2 100
a. Analyze the above output to determine the regression equation.
b. Find and interpret β˖1in the context of this problem.
c. Find and interpret the coefficient of determination (rsquared).
d. Find and interpret coefficient of correlation.
e. Does the data provide significant evidence (a = .05) that the size of the production run can be used to predict the total labor hours? Test the utility of this model using a twotailed test. Find the observed pvalue and interpret.
f. Find the 95% confidence interval for the mean total labor hours for all occurrences of having production runs of size 60. Interpret this interval.
g. Find the 95% prediction interval for the total labor hours for one occurrence of a production run of size 60. Interpret this interval.
h. What can we say about the total labor hours when we had a production run of size 100?
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