Question

Q.4.12. Typographical errors. Shown below are the number of galleys for a manuscript (X) and the total dollar cost of correcting typographical errors (Y) i a random sample of recent

orders handled by a firm specializing in technical manuscripts. Since Y involves variable costs only, an analyst wished to determine whether regression-through-the-origin model (4.10) is appropriate for studying the relation between the two variables.

i: 1 2 3 4 5 6 7 8 9 10 11 12

Xi: 7 12 10 10 14 25 30 25 18 10 4 6

Yi: 128 213 191 178 250 446 540 457 324 177 75 107

a. Fit regression model (4.10) and state the estimated regression function.

b. Plot the estimated regression function and the data. Does a linear regression function through the origin appear to provide a good fit here? Comment.

Answer 1

a.

Sum of X = 171
Sum of Y = 3086
Mean X = 14.25
Mean Y = 257.1667
Sum of squares (SS_X) = 778.25
Sum of products (SP) = 13985.5

Regression Equation = ŷ = bX + a

b = SP/SS_X = 13985.5/778.25 = 17.9705

a = M_Y - bM_X = 257.17 - (17.97*14.25) = 1.0878

ŷ = 17.9705X + 1.0878

b.

As all the points lie on the line we conclude that it is a good fit.