y = ax Insert Page Layout Review Home Formulas Data A Cumulative Cumulative Cumulative Avg DLH (y) 21 Output (x) DLH Month LN (y) LN (x) 0.716 6.528 22 January 23 February 24 March 25 April 26 May 27 June 28 July 29 August 30 September 31 October 32 November 33 December 684 1,400 2.047 2,220 1.888 0.635 7.070 1,176 1,836 3,095 3,765 1.686 0.522 7.515 2,340 2,952 1.609 0.476 7.758 4,525 1.533 0.427 7.990 3,588 5,290 1.474 0.388 8.185 1.422 4,236 6,025 0.352 8.351 4,836 6,685 1.382 0.324 8.484 5,484 6,180 7,380 1.346 0.297 8.610 8,090 1.309 0.269 8.729 6,852 7,527 8,780 9,480 1.281 0.248 8.832 0.231 8.926 1.259 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: Regression 1: Ln (Cumulative avg DLH per unit) = a + [b x Ln (Cumulative Output)] Variable Coefficient Standard Error t-Value Constant 2.087 0.024 85.44 Independent variable: Ln (Cum Output) -0.208 0.003 -69.046 p2 = 0.998; Durbin-Watson statistic = 2.66 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 ex- pected output of 650 units in January 2018? How confident is she of this new cost estimate?
Cost estimation, learning
where x is cumulative production in units, y 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:
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