Question

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An accountant wishes to predict direct labor cost() on the basis of the batch size (x) of a product produced in a job shop. Data for 12 production runs are given in the table below, along with the Excel output from fitting a least squares regression line to the data. Direct Labor Cost Data Direct Labor Batch Cost, y ($100s) Size, x 619 72 894 626 751 948 979 262 423 198 697 658 122 Batch Size Fit Plot Labour Cost = 250.6179 +6.5354' B Size Labour cost (a) Find be and bo. (Round your intermediate value and final answers to 4 decimal places. Negative amounts should be indicated by a minus sign.) bo (b) Interpret the meanings of bo and by. Does the interpretation of bo make practical sense?

Answer 1

(% 619 )' (1) July 72 22 751 916 979 262 423 198 69+ 658 15 52 81 58 122 Tax 1177 Exi. 638 / 31 = nbigsols teulat | 2 61616. 14.4 Now, j = {xi go - 1593.9161 x= {xi = 688 168.1667) n 12 K(Y) syy) v(x) = $(x-7)72843671 a) her the neguession equation of you x be: y= bot box 51616. 1667 wolene, 6 = S(yi-V) (x->) - Book och Bob. 198 8687.673 (x1 - x)² 6 .53591 auw, bo = 7 - 6,8 = (593.1167) - (6.6367) (53,1667) or, 5o = 1250.6179]

b) b₁ is the estimated increase in Direct Labor Cost for every 1 unit increase in batch size.

    b₀ is the estimated Direct Labor Cost when batch size = 0

c) y_hat = 250.6179 + 6.534x

d) y_hat(60) = 250.6179 + 6.534(60) = 642.658

NOTE:

1) Y_bar = 593.9167, X_bar = 53.1667, Σ(X_i - X_bar)² = 8681.677, Σ(Y_i - Y_bar)² = 896108.9167, Σ(X_iY_i - X_bar Y_bar)= 54646.1667

2) I have left empty cells as they can be calculated easily.