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(tco e) the central company manufactures a certain item once a week

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(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 person-hours 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
P-Value = 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   R-Sq = 98.1%   R-Sq(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 (r-squared).
d. Find and interpret coefficient of correlation. 
e. Does the data provide significant evidence (= .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 two-tailed test. Find the observed p-value 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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