Question

You have been asked to engage in one final project for the chain of department stores for which you have been working concerning the sales of a type of shirt that they carry. Specifically, this time you wish to study the nature of the relationship between the average daily number of hours the stores are open and monthly sales for the month you have been studying. You wish to utilize the average daily number of hours the stores are open as a variable designed to predict and explain sales of the item in this month. Data concerning these two variables of interest is collected from a random sample of stores throughout the chain of stores. This data is shown on the next page. Various questions will be asked and then need to be answered about the results you generate. These questions follow the presentation of the data. You should answer the questions posed in a memo that will accompany your results. Where appropriate, be sure to annotate the printouts you include as a part of the work you have accomplished.

Data: Number of Hours Sales

14 348

12 355

9 325

10 401

22 455

20 398

18 288

17 350

13 380

19 438

18 386

23 430

19 320

20 489

11 354

22 480

17 420

19 456

9 289

15 376

13 337

11 306

f)          Find the sample coefficient of determination for the above data. Explain its meaning relative to the problem.

g)        Find the adjusted sample coefficient of determination for the above data. Explain its meaning relative to the problem. Why does it differ, if it does, from the coefficient of determination that you found in the previous part of the problem?

h)        Find the sample standard error of the estimate for the above data. Explain its meaning relative to the problem.

i) Find the sample coefficient of correlation for the above data. Explain its meaning relative to the problem.

j)          Perform a complete residual analysis on this sample data to decide of the method of least squares is an appropriate way to analyze the data of this model. Be sure to address all aspects of a good residual analysis. Be sure to provide all the necessary printouts to do this. Include a check for the presence of autocorrelation at the 1% level of significance.

Hint: d_L = 1.00 and d_U = 1.17

Answer 1

Answer to the question)
Enter the data in excel

Click Data tab

Click on regression

click ok

the regression window shows up:

Regression Input Sales Hours OK $D$2:$D$24 $C$2 : $C$24 Constant is Zero Input Y Range: Input X Range: Labels 14 12 9 10 348 355 325 401 455 398 288 350 380 438 386 430 320 489 354 480 420 456 289 376 337 306 Cancel Help Confidence Level: 95 20 18 17 13 19 18 23 19 20 Output options Output Range New Worksheet Ply: O New Workbook Residuals Residuals Standardized Residuals Residual Line Fit Plots Normal Probability Normal Probability Plots 17 19 9 15 13

.

Input Y range as sales data

Input X range as hours data

tick mark the check box next to labels

Tick mark for residuals and residual plots

Click OK

The following output appears on screen:

SUMMARY OUTPUT Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ←-coefficient of correlation r = 0.6555987 L 0.65599 0.43032 0.40183 46.3626 Coefficient of determination R square Adjusted coeff of determination Standard error value ←

.Answer f: coefficient of determination = R square = 0.43032

Answer g: adjusted value = 0.40183

Answer h : standard error = 46.3626

Answer i: Coefficient of correlation = 0.65599