Question

You are a business analyst for Dr. Clark's Premium Soft Drink Company. Your boss, the beloved Dr. Clark, wants to know if there is any relationship between the price per six pack and the number of cases sold and if so what is it. The Excel data set attached to this problem contains the prices for per six pack and the number of cases sold of Dr. Clark's Premium Soft Drinks. The data were collected over a 52 week period. Write a back story given the above information. Make sure to submit both your word document and Excel worksheet.

1 Week Price per si pack Cases sold 99 447 .99 430 .99455 9.99489 .99 627 .99 558 .99 476 10.05631 10.06 434 0.07 419 10.07 454 10.06433 10.06 338 0.07 356 10.07 603 10.07 533 0.07 365 10.07318 0.07 571 0.07 720 0.07 526 9.59 887 7.39 2203 8.02 1628 0.06 730 .88 1020 9.831161 9.85 502 0.06 474 10.06 605 10.07 459 10.07 377 7.57 1591 7.17 3113 8.12 1615 .97 486 0.53 403 10.60 588 10.62441 0.06511 7.37 1841 7.29 1460 7.97 525 10.35419 79 566 9.80 525 7 620 10.64557 7.28 1483 7.20 2632 8.41 898 .931010

Following the outline and procedures of a correctly done preliminary report make sure you address the following questions;

1) What statistical procedure did you choose and why?

2) Based on your learning at Warner what did you hypothesize the relationship between the two variables (price and quantity) and why?

3) Write out the regression equation.

4) To prove to your Beloved Boss that you know what your are doing explain to him

a) What is the R² is and means? Why is it good or not?

b) What is the standard error of the estimate?

c) Conduct a global test of the hypothesis that all parameters are equal to zero.

d) Are the coefficients significant at the α=0.05?

5) What happens to cases sold for every $1.00 change in the price per six pack?

56 The Beloved Boss wants to know what, if possible, how many cases would be sold at a price $11.00 per six pack

Week

(1-52)

Price Per six pack

9.99
9.99
9.99
9.99
9.99
9.99
9.99
10.05
10.06
10.07
10.07
10.06
10.06
10.07
10.07
10.07
10.07
10.07
10.07
10.07
10.07
9.59
7.39
8.02
10.06
9.88
9.83
9.85
10.06
10.06
10.07
10.07
7.57
7.17
8.12
9.97
10.53
10.60
10.62
10.06
7.37
7.29
7.97
10.35
9.79
9.80
9.97
10.64
7.28
7.20
8.41
9.93

cases Sold

447
430
455
489
627
558
476
631
434
419
454
433
338
356
603
533
365
318
571
720
526
887
2203
1628
730
1020
1161
502
474
605
459
377
1591
3113
1615
486
403
588
441
511
1841
1460
525
419
566
525
620
557
1483
2632
898
1010

Answer 1

STOF > price 111 9.99 [13] 10.06 10.07 10.07 10.07 10.07 10.07 10.07 10.07 10.07 9.59 7.39 8.0:2 [25] 10.06 9.88 9.83 9.85 10.06 10.06 10.07 10.07 7.57 7.17 8.12 9.97 [371 10.53 10.60 10.62 10.06 7.37 7.29 7.97 10.35 9.79 9.80 9.97 10.64 [491 7.28 7.20 8.41 9.93 9.99 9.99 9.99 9.99 9.99 9.99 10.05 10.06 10.07 10.07 10.06 quantity [1] 447 430 455 489 627 558 476 631 434 419 454 433 338 356 603 [16] 533 365 318 571 720 526 887 2203 1628 730 1020 1161 502 474 605 (311 459 377 1591 3113 1615 486 403 588 441 511 1841 1460 525 419 566 [461 525 620 557 1483 2632 898 1010 cor (price, quantity) [1] -0.8586632 > fitl-1m(quantity price) summary (fiti) Call: 1m (formula quantity price) Residuals: Min 1Q Median 30 Max -1057.69 -133.88-35.85 97.69 1132.10 Coefficients: Estimate Std. Error t value Pr(기디) (Intercept) 5549.87403.45 13.76 < 2e-16xx price -497.76 42.02 -11.85 3.98e-16 *x Signif. codes: 0 0.001 0.01 0.05' 0.1 1 Residual standard error: 313.2 on 50 degrees of freedom Multiple R-squared: 0.7373, Adjusted R-squared: 0.732 F-statistic: 140:3 on 1 and 50 DF, p-value: 3.98e-16

O first we need ho cam pute correlahion coeff Because clark coant to tnoco relahionship Tt is-0853

Regression Eq quanhhy 5549.9-491.8 Pice 13 2 of variabion in solds is explained by price pex six pack SE (4202 ) From summaru table in R-outpc T testS 1:85 value- .98 10 which is much tess han &o oS hence cwe seiect Ho lt- ,-is-significant Tf (eincrease quanhity sold decreased by 497 8 Tf cwe decrcast price by 1$ thtn 487-& quanhisold increased