Question

Cubic Feet Moved 491 453 407 342 589 599 Labor Hours 30.00 27.75 23.25 22.00 29.50 35.75 28.00 20.25 28.50 28.25 42.75 37.00 34.00 42.00 27.25 45.75 29.00 45.00 337 571 547 810 659 781 471 774 477 805

Answer 1

• Regression and Residual Analysis using Excel:

1.Enter the data into Excel sheet.

2.If this is the first time you have used an Excel add-in, click the File tab, otherwise skip to step 7.

3.Click Options from the list on the left.

4.Select Add-ins in the Excel Options box.

5.In the Add-in list box, select Analysis Toolbox-VBA from the Inactive Application Add-ins list.

6.Click OK.

7.Then select Data/ Data Analysis tab from the menu bar.

8.The Data Analysis dialog box will appear on the screen.

9.From the Data Analysis dialog box, select Regression and click OK.

10.The Regression dialog box will appear on the screen.

11.Place independent variables (GPA) in Input X Range and place dependent variable (Hours) in Input Y Range.

12.Place appropriate confidence level in Confidence Level box. (If necessary)

13.Click on Residuals, Residual Plots

14.Click OK.

By performing residual analysis the partial output:

Observation	Predicted Labor Hours	Residuals
1	28.00573	1.994273
2	26.03057	1.719434
3	23.63958	-0.38958
4	20.26102	1.738982
5	33.09956	-3.59956
6	33.61934	2.130658
7	31.33231	-3.33231
8	20.00113	0.248872
9	32.16396	-3.66396
10	30.91649	-2.66649
11	44.58668	-1.83668
12	36.73802	0.261983
13	31.33231	2.667686
14	43.07932	-1.07932
15	26.96617	0.283831
16	42.71548	3.034523
17	27.27804	1.721964
18	44.32679	0.673207
19	16.98641	-1.73641
20	38.92109	1.828911

1) Checking for Linearity:

The residual plot is,

From above plot, it can be seen that all the points lie withing a certain band. Therefore the assumption of linearity does not violated.

2) Checking for Normality:

The normal probability plot is given as:

From the above plot, it can be seen that the given data does not violate the assumption of normality.

3) Checking for Independence:

Since it is known that the residuals sum to zero, they are not independent.

From above output, Sum of Residuals = 0

Therefore, the assumption of independence is violated.

4) Checking for Equal Variance:

Plot residuals against fitted values (in most cases, these are the estimated conditional means, according to the model), since it is not uncommon for conditional variances to depend on conditional means, especially to increase as conditional means increase. (This would show up as a funnel or megaphone shape to the residual plot.)

From the above plot, it is seen that it is not a funnel shaped. Therefore assumption of equal variance is violated.

• Answer:

The following assumptions of regression are seriously violated: (Correct options)

(c) The assumption of independence has been violated because errors from later time periods appear to be related to these from earlier time periods.

(d) The assumption of equal variance has been violated because the variability of the residuals is much greater when the number of customers is larger.