Inbee is concerned that she still does not understand the relationship between output and labor consumption. She consults with Jim Park, the head of engineering, and shares the results of her regression estimation. Jim indicates that the production of new smartphone models exhibits significant learning effects—as Hankuk gains experience with production, it can produce additional units using less time. He suggests that it is more appropriate to specify the following relationship:

y = axb

where x is cumulative production in units, y is the cumulative average direct labor-hours per unit (i. e., cu-mulative DLH divided by cumulative production), and a and b are parameters of the learning effect. To estimate this, Inbee and Jim use the original data to calculate the cumulative output and cumulative average labor-hours per unit for each month. They then take natural logarithms of these variables in order to be able to estimate a regression equation. Here is the transformed data:

1. Estimate the relationship between the cumulative average direct labor-hours per unit and cumulative output (both in logarithms). Verify that the following is the result obtained by Inbee and Jim:
Regression 1: Ln (Cumulative avg DLH per unit) = a + [b * Ln(Cumulative Output)]

2. Plot the data and regression line for the above estimation. Evaluate the regression using the criteria of economic plausibility, goodness of fit, and slope of the regression line.
3. Verify that the estimated slope coefficient corresponds to an 86.6% cumulative average-time learning curve.
4. Based on this new estimation, how will Inbee revise her budget for Hankuk’s variable cost for the ­expected output of 650 units in January 2014? How confident is she of this new costestimate?

Cumulative Cumulative Output Cumulative Avg DLH DLH LN LN(x) 2047 0.716 6.528 February7 2,220 1888 0635 7.070 1686 0.522 7.515 1.609 0.476 7.758 May2952 4 1533 0427 7.990 1474 0.388 8.185 uly4,236 6,025 1422 0.352 8.351 1382 0.324 8.484 1346 0297 8610 1309 0.269 8.729 1281 0.248 8.832 December7,527 9,4801259 0231 8.926 Month January684 1400 March 1,836 2,340 3,765 4,525 June 3588 August 48366685 1 Septembe 5,484 7,380 1 October November 6,852 1 8,090 8,780 6,180 Coefficient Standard Error Value 85.44 69.046 Variable Constant 2.087 0.024 Independent variable: Ln (Cum Output) -0.208 0.003 0054; Durbin-Watson statistic 2.66