Cost estimation, learning curves (continuation of 10-44). 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:

where  is cumulative production in units,  is the cumulative average direct labor-hours per unit (i.e., cumulative 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:

Required

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:

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 2018? How confident is she of this new cost estimate?

Continuation of 10-44

Cost estimation. Hankuk Electronics started production on a sophisticated new smartphone running the Android operating system in January 2017. Given the razor-thin margins in the consumer electronics industry, Hankuk’s success depends heavily on being able to produce the phone as economically as possible.
At the end of the first year of production, Hankuk’s controller, Inbee Kim, gathered data on its monthly levels of output, as well as monthly consumption of direct labor-hours (DLH). Inbee views labor-hours as the key driver of Hankuk’s direct and overhead costs. The information collected by Inbee is provided below:

Required

1. Inbee is keen to examine the relationship between direct labor consumption and output levels. She decides to estimate this relationship using a simple linear regression based on the monthly data. Verify that the following is the result obtained by Inbee:

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. Inbee estimates that Hankuk has a variable cost of $17.50 per direct labor-hour. She expects that Hankuk will produce 650 units in the next month, January 2018. What should she budget as the expected variable cost? How confident is she of her estimate?