The Manufacturing database associated with this text and found in WIleyPLUS has
ID: 3322544 • Letter: T
Question
The Manufacturing database associated with this text and found in WIleyPLUS has a variable, value of Industrial Shipments, that is coded 0 if the value is small and 1 if the value is large. Using Minitab, a logistic regression analysis was done in an attempt to predict the value of industrial shipments by the number of production workers. The minitab output is given below. Study the output. What is the model? How good is the overall fit of the model? Comment on the strength of the predictor. Use the model to estimate the probability that a selected company has a large value of industrial shipments if their number of production workers is 30.
Logistic Regression Table
Odds
95%
CI
Predictor
Coef
SE Coef
Z
P
Ratio
Lower
Upper
Constant
-3.07942
0.535638
-5.75
0.000
No. Prod. Wkrs.
0.0544532
0.0096833
5.62
0.000
1.06
1.04
1.08
Log-Likelihood = -48.166
Test that all slopes are zero: G = 97.492, DF = 1, P-Value = 0.000
The answer is y^ =-3.07942 + 0.054432 production workers, G =97.492, p-value =0.000. overall, there is statistical significance. Number of production workers is significant at a =.001 and has a p-value of 0.000. predicted value equals -1.445824. prob. =.19 of being a large company.
Solve it step by step with calculation do not use excel or other program only calculation is accepted
Logistic Regression Table
Odds
95%
CI
Predictor
Coef
SE Coef
Z
P
Ratio
Lower
Upper
Constant
-3.07942
0.535638
-5.75
0.000
No. Prod. Wkrs.
0.0544532
0.0096833
5.62
0.000
1.06
1.04
1.08
Log-Likelihood = -48.166
Test that all slopes are zero: G = 97.492, DF = 1, P-Value = 0.000
Explanation / Answer
What is the model?
y^ = -3.07942 + 0.054432*x {look at coeff column)
How good is the overall fit of the model? Comment on the strength of the predictor
P-Value = 0.000 {last line
p-value < 0.01
hence significant
Use the model to estimate the probability that a selected company has a large value of industrial shipments if their number of production workers is 30.
when x = 30
y^ = -3.07942 + 0.054432*30 = -1.44646
p = 1 /(1 + e^(-y^))
= 1/(1 + e^(1.44646))
= 0.190546
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