Question

Month Machine Hours (hrs.) Maintenance Costs ($) 1 1,330 102,694 2 1,400 103,694 3 1,500 108,694 4 1,470 108,694 5 1,620 116,694 6 1,690 115,694 7 1,490 107,694 8 1,310 102,694 9 1,450 106,694 10 1,580 113,694 11 1,300 100,694 12 1,600 113,694 13 1,650 114,694 14 1,440 109,694 15 1,340 102,694 16 1,670 114,694 17 1,480 106,694 18 1,360 103,694 19 1,340 103,694 20 1,540 112,694

Assume that the following relationship holds:

Maintenance Costs = (v * Machine Hours) + f

REQUIRED

Estimate the values of v and f and the cost equation, using,

1. The Linear Regression method.

Note, to use the linear regression method, you MUST use the Microsoft Excel program.

Make sure to report

1. The values of v and f;

2. A scatter plot of the data points, and

3. The adjusted R-square; explain what the adjusted R-square means.

4. The cost equation in the form of Y = vx + f, substituting the values for v and f from the regression output.

YOUR SUBMISSION MUST BE IN EXCEL.

Answer 1

Adjusted R-square is a modified version of r², adjusted for the number of predictors in the regression model. It compares the explanatory/predictor power of regression models having different number of predictors.

Adjusted r-squared value,

where, n is the number of data points and k is the number of independent variables,

In this case, n = 20, and k = 1 (Machine hours is the independent variable)

Adjusted r-squared value = 1 - (1-0.9342)*(20-1)/(20-1-1) = 0.9305