A lead inspector at ElectroTech, an electronics assembly shop, wants to convince

Question

A lead inspector at ElectroTech, an electronics assembly shop, wants to convince management that it takes longer, on a per-component basis, to inspect large devices with many components than it does to inspect small devices because it is difficult to keep track of which components have already been inspected. To prove her point, she has collected data from the last 25 devices. The data are shown in the accompanying table Number of Components on Device Inspection Time (seconds) 13 30 15 51 24 42 12 19 42 63 26 80 30 12 31 19 52 60 72 102 59 19 25 16 13 21 12 23 67 70 a. A scatterplot of the above data is shown below. Does the lead inspector's claim seem credible? Yes O No b-1. Estimate the linear, quadratic, and cubic regression models. Report the Adjusted R2 for each model. (Round your answers to 4 decimal places.) usted R2 Linear model Quadratic model Cubic model b-2. Which model has the best fit? Linear model O Quadratic model O Cubic model c. Use the best model to predict the time required to inspect a device with 35 components. (Round your answer to 2 decimal places.) Time required

Explanation / Answer

a. From the scatter plot its clear that inspector claim, higher number of components require longer time is correct.

Since there is an increasing trend.

b1. The fitted linear regression equation of Inspection time (y) on x (no. of components) is

Y = 18.7876 + 2.0629 * x ; Y is the predicted value of y ; adjusted R-squared = 0.9261

The fitted quadratic regression equation of y on x is

Y = 57.24 + 98.2373 * x - 22.2242 * x^2 ; adjusted R-squared = 0.9746

b2. Adjusted R-squared is slightly higher for quadratic model we choose the linear one for its simplicity or parsimony.

c. Using the best model the predicted value inspection time when the no. of components is 35 is

18.7876 + 2.0629 * 35 = 90.99  

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