the central company manufactures a certain item once a week a vast range of online homework help to choose from

the central company manufactures a certain item once a week a vast range of online homework help to choose from

(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.

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SIZELABORPREDICT
408360
3060100
70138 
90180 
5097 
60118 
70140 
4075 
80159 
70140 
4075 
80159 
70144 
5090 
60125 
5087 

 
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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