A production manager wishes to examine the relationship between unit production

Question

A production manager wishes to examine the relationship between unit production (number of units produced) and associated costs (total cost). The accompanying data table contains data for 10 months of production. Using these data, perform a natural logarithm transformation of the dependent variable (total cost). Using the transformed dependent variable and the unit production as the independent variable, perform a regression analysis. Complete parts (a) through (d) below. Please help. Thanks so much in advance

a) State the regression equation:

b) Determine the test statistic.

c) The coefficient of determination indicates that ____% of the variation in _____ can be explained by variation in _______

d) Compute the adjusted r squared .

Units Total_Cost_($)

20 17608

40 20790

60 29464

80 40271

100 43859

120 55543

140 62129

160 67472

180 65809

200 69641

Explanation / Answer

Line of Regression Y on X i.e Y = bo + b1 X

calculation procedure for regression

mean of X = X / n = 110

mean of Y = Y / n = 47258.6

(Xi - Mean)^2 = 33000

(Yi - Mean)^2 = 3500207278.4

(Xi-Mean)*(Yi-Mean) = 10507280

b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2

= 10507280 / 33000

= 318.40242

bo = Y / n - b1 * X / n

bo = 47258.6 - 318.40242*110 = 12234.33333

value of regression equation is, Y = bo + b1 X

Y'=12234.33333+318.40242* X

Use MINITAB software to construct a transformed regression equation.
MINITAB procedure:
Step 1: Choose Stat> Regression> Regression.
Step 2: In Response. enter In(calories).
Step 3: In Predictors. enter Alcohol% and Carbohydrates.
SteD 4: Click OK.

————— 21-03-2018 11:17:39 PM ————————————————————

Welcome to Minitab, press F1 for help.

Regression Analysis: Total_Cost versus Units

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 1 3345543424 3345543424 173.05 0.000
Units 1 3345543424 3345543424 173.05 0.000
Error 8 154663854 19332982
Total 9 3500207278

Model Summary

S R-sq R-sq(adj) R-sq(pred)
4396.93 95.58% 95.03% 92.56%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant 12234 3004 4.07 0.004
Units 318.4 24.2 13.15 0.000 1.00

Regression Equation

Total_Cost = 12234 + 318.4 Units

a) State the regression equation:
Total_Cost = 12234 + 318.4 Units

b) Determine the test statistic.
t=13.15

c) The coefficient of determination = 95.58%

d) Compute the adjusted r squared .
adjusted r^2 = 95.03

X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 20 17608 8100 879158080 2668554 40 20790 4900 700586786 1852802 60 29464 2500 316647789 889730 80 40271 900 48826554 209628 100 43859 100 11557280 33996 120 55543 100 68631283 82844 140 62129 900 221128796 446112 160 67472 2500 408581540 1010670 180 65809 4900 344117340 1298528 200 69641 8100 500971830 2014416

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