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Thompson Machine Works Regression Problem

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Thompson Machine Works purchased several new, highly sophisticated machines. The production department needed some guidance with respect to qualifications needed by an operator. Is age a factor? Is the length of service as a machine operator important? In order to explore further the factors needed to estimate performance on the new machines, four variables were listed:
X1 _ Length of time employee was a machinist. X3 _ Prior on-the-job rating.
X2 _ Mechanical aptitude test score. X4 _ Age.
Performance on the new machine is designated Y.Thirty machinists were selected at
random. Data were collected for each, and their performances on the new machines
were recorded. A few results are listed in the attached file.

The equation is: Y _ 11.6 _ 0.4X1 _ 0.286X2 _ 0.112X3 _ 0.002X4
a. What is the full designation of the equation?
b. How many dependent variables are there? Independent variables?
c. What is the number 0.286 called?
d. As age increases by one year, how much does estimated performance on the new machine increase?
e. Carl Knox applied for a job on a new machine. He has been a machinist for six years, and scored 280 on the mechanical aptitude test. Carl's prior on-the-job performance rating is 97, and he is 35 years old. Estimate Carl's performance on the new machine.

See attached file for full problem description.

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Solution Summary

This provides a solution to a regression problem.

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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