Question

The operations manager at an electronics company believes that the time required for workers to build a circuit board is not necessarily proportional to the number of parts that go onto the board. She has collected data on the time (in minutes) it takes a worker to build a board and the number of parts installed. The data is in a worksheet names Circuits.   Data-1.xlsx

Time	Parts
30.8	62
9.8	32
61.4	96
9.0	30
25.8	53
56.7	94
29.5	59
25.4	53
51.4	87
14.9	41
35.6	71
17.2	43
40.2	73
6.5	25
8.0	28
55.2	92
21.9	51
22.2	51
14.5	41
6.0	24
49.0	85
9.6	32
30.4	61
17.5	43
29.8	60

1. Estimate a regression line to predict time based on the number of parts.  What is the Coefficient of Determination of the simple regression? (enter as a decimal)

3. What is the standard error of the estimate of the simple regression?

4. What is the predicted time to build a circuit board with 50 parts?

5. Estimate a quadratic regression line to predict time based on the number of parts and the number of parts squared. What is the Coefficient of Determination of the quadratic model? (enter as a decimal)

6.What is the standard error of the estimate of the quadratic model?

7.

Which model is better, the simple regression or the quadratic?

Group of answer choices

a.Simple because the MSR is larger.

b. Simple because the t-statistic of Parts is much higher.

c.Quadratic because standard error is lower and adj-R² is higher.

d. Quadratic because it has two variables instead of one.

Answer 1

Ques 1 ) Regression Equation/Line – Simple Regression Model :

Time = -14.4886 + 0.750192 * Parts

Coefficient of Determination(R squared) – Simple Regression Model = 0.991993215

Ques 3 ) Standard Error of estimate = 1.551506

Ques 4 ) Predicted Time to build a circuit board with 50 parts :

Time = -14.4886 + 0.750192 * Parts

Time = -14.4886 + 0.750192 * 30

Time = 8.017116

Ques 5 ) Regression Equation/Line – Quadratic Regression Model

Time = -6.716542633 + 0.002528168 * (Parts^2) + 0.447625 * Parts

Coefficient of Determination(R squared) – Quadratic Regression Model = 0.996601

Ques 6 ) Standard Error of estimate - Quadratic Regression Model = 0.989543

Ques 7 ) C . Quadratic because standard error is lower and adj-R2 is higher.

Any regression output with R squared value and lower standard error is better.

Steps to perform Regression

Step 1: Choose “Data Analysis” from the “Data” tab in Excel

Step 2: Select “Regression” & click “OK.”

Step 3: Select Input Range for dependent(Time) and independent(Parts) in case of simple regression and in case of quadratic Model dependent(Time) and independent(Parts and Parts^2) .

Step 5: In the Output range box ,select a cell location where you want result.

Step 6: Click “OK.”

Regression Outputs :