Question

Number of Components Inspection Time 31 83 14 49 8 30 17 60 15 50 10 41 23 72 43 98 6 23 12 41 20 63 9 26 31 80 13 49 12 30 20 62 18 52 18 60 24 72 45 101 16 58 14 44 20 67 12 46 22 69 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 on the inspection time (Time in seconds) and the number of components per device (Components) from the last 25 devices. A portion of the data is shown in the accompanying table. Estimate the linear, quadratic, and cubic regression models. Report the Adjusted R2 for each model. (Round answers to 4 decimal places.) Which model has the best fit? Cubic model Quadratic model Linear model Use the best model to predict the time required to inspect a device with 38 components. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.) seconds

Answer 1

First Enter the data into MS-Excel:

Now Make a Scatter-plot between Number of Components and Inspection Time.

Steps in Excel:

First Select all Data:

Insert-->then click on the Scatter in Charts Groups:

Linear Regression:

Now Right-Click on the anyone of the point then new tab open.

Then New click on the Add Trendline again new tab open like that:

So Click on Linear:

Then tick the Display Equation on chart and Display R-squared value on chart:

Then Click on Close:

Then We can the Equation and R squared Value:

Quadratic Regression:

Now do again the same thing, but for Quadratic Regression model:

Select the Polynomial and order 2, for Quadratic Regression Model:

And Tick Display the Equation and R squared value on chart and then close the tab.

Now Scatter-Plot:

Cubic Regression:

Select the Polynomial and order 3, for Cubic Regression Model:

And Tick Display the Equation and R squared value on chart and then close the tab.

Now Scatter-Plot:

Result:

From all regression model Cubic Regression Model giving maximum R-squared Value.

So Cubic Regression Model is best Fit:

Given:

Number of Components (x) = 38

Time(y) = 0.0008x³ - 0.0966x² + 5.1994x - 7.559

put x =38 in Cubic Regression model:

Time(y) = 0.0008*(38)³ - 0.0966*(38)² + 5.1994*38 - 7.559

After calculation:

Time(y) = 42.8976 - 139.4904 + 197.5772 - 7.559

Time(y) = 93.4254

Round to 2 decimal:

Time(y) = 93.43