(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 (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?

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