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Regression | Statistics homework help


Data: Production costs of custom metal blanks that are used for computer aided machining.  A 3D printed design is sent to the manufacturer which is used to arrive at a cost/unit and that estimate is used for pricing decisions.   We are going to help the manufacturer by helping him analyze some factors influencing the cost of custom blanks production.  Show all the supporting output.  I prefer you use JMP Pro for the assignment.

N: 195 observations from a manufacturer.  

FILENAME/Dataset: mgfproduction_assignment 1.jmp Download mgfproduction_assignment 1.jmp 

Instructions:  Load the file into Jmp.  Make sure you note that N=195 observations.  There should 12 columns.    Make sure that the specification of only 3 variables Detail, Rush, Plant is set as “categorical”. You should see a red histogram for these variables.  All other variables should be continuous-blue triangle.   For this part of the assignment, focus only on 2 variables:  cost/unit (Average cost/unit) and material cost/unit (materials are just one part of any manufacturer’s production cost).

  1. (15 points) Analyze the 2 variables- $Average cost/unit and $Material cost/unit :
    1. Visualize the relation: scatter plots (5)
    2. Visualize and analyze distributions of each of the variables. (5)
    3. Document the simple correlation coefficient and the mnemonics (mean and standard deviation) of Average cost/unit and Material cost per unit. (5)  (Note, if you click the Distribution icon (green parallel bars on the tool menu next to Fit y by x).

This is best practice for any data and should be the first step of analysis.

  1. (85) Fit the simple linear regression model Y=Average cost/unit on X= Material cost/unit.   E(Y=Average cos/unit |material cost/unit)
    1. What portion of Y does the material cost explain? Is this significant?  (10)
    2. What is the 95% confidence interval for the coefficient of material costs? (10). Explain.
    3. What about the 99% confidence interval? When confidence level is increased to 99% does the parameter estimate lie in the 99% confidence interval? (10)
    4. Is this regression significant- what is the global fit of this regression? (10)
    5. What is the prediction equation for this regression? (10).  What does this say?  Explain.
    6. Predict the change in $average cost/unit (Y) when material cost/unit is $2/unit versus $1.60/unit.  (10)
    7. Can you give the confidence interval for E(Y=Average cost/unit) when material cost =$1.60? (95% confidence interval). (12.5)
    8. Can you give the prediction interval for Y hat when material cost =$1.60? (95% confidence interval). (12.5)

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