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 (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 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?