# ANOVA, Correlation & Regression

Chapter 11: Section Exercises #3, 4, 6, 14 , 16

NO P-Values are necessary for these problems

11.3 Semester GPAs are compared for seven randomly chosen students in each class level at Oxnard

University. Does the data prove a significant difference in mean GPAs? GPA1

GPA for Randomly Selected Students in Four Business Majors

Accounting Finance Human Resources Marketing

2.48 3.16 2.93 3.54

2.19 3.01 2.89 3.71

2.62 3.07 3.48 2.94

3.15 2.88 3.33 3.46

3.56 3.33 3.53 3.50

2.53 2.87 2.95 3.25

3.31 2.85 3.58 3.20

11.4 Sales of People magazine are compared over a 5-week period at four Borders outlets in Chicago.

Does the data prove a significant difference in mean weekly sales? Magazines

Weekly Sales

Store 1 Store 2 Store 3 Store 4

102 97 89 100

106 77 91 116

105 82 75 87

115 80 106 102

112 101 94 100

11.6 Refer to Exercise 11.2. Which pairs of mean examination times differ significantly (4 physicians)?

Physicians

11.2 One particular morning, the length of time spent in the examination rooms is recorded for each

patient seen by each physician at an orthopedic clinic. Does the data prove a significant difference

in mean times? Physicians

Time in Exam Rooms (Minutes)FIGURE 11.12

Physician 1 Physician 2 Physician 3 Physician 4

34 33 17 28

25 35 30 33

27 31 30 31

31 31 26 27

26 42 32 32

34 33 28 33

21 26 40

29

11.14 Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by

using different types of fuel. One vehicle of each size is tested. Does this sample prove that there

is a significant difference in treatment means? MPG2

87 Octane 89 Octane 91 Octane Ethanol 5% Ethanol 10%

Compact 27.2 30.0 30.3 26.8 25.8

Mid-Size 23.0 25.6 28.6 26.6 23.3

Full-Size 21.4 22.5 22.2 18.9 20.8

SUV 18.7 24.1 22.1 18.7 17.4

11.16 A beer distributor is comparing quarterly sales of Coors Light (number of six-packs sold) at

three convenience stores. Does this sample prove a significant difference in treatment means?

BeerSales

Store 1 Store 2 Store 3

Qtr 1 1,521 1,298 1,708

Qtr 2 1,396 1,492 1,382

Qtr 3 1,178 1,052 1,132

Qtr 4 1,730 1,659 1,851

Chapter 12: Section Exercise #2, 4, 6, 8, 10

Instructions for Exercises 12.2 and 12.3: (a) Make an Excel scatter plot. What does it suggest about

the population correlation between X and Y? (b) Make an Excel worksheet to calculate SSxx , SSyy , and

SSxy . Use these sums to calculate the sample correlation coefficient. Check your work by using Excel's

function =CORREL(array1,array2). (c) Use Appendix D to find t.05 for a two-tailed test for zero correlation.

(d) Calculate the t test statistic. Can you reject ρ = 0? (e) Use Excel's function =TDIST(t,deg_freedom,tails)

to calculate the two-tail p-value.

12.2 Part-Time Weekly Earnings ($) by College Students WeekPay

Hours Worked (X) Weekly Pay (Y)

10 93

15 171

20 204

20 156

35 261

Instructions for Exercises 12.4-12.6: (a) Make a scatter plot of the data. What does it suggest about the

correlation between X and Y? (b) Use Excel, MegaStat, or MINITAB to calculate the correlation coefficient.

(c) Use Excel or Appendix D to find t.05 for a two-tailed test. (d) Calculate the t test statistic.

(e) Calculate the critical value of rα. (f) Can you reject ρ = 0?

12.4 Moviegoer Spending ($) on Snacks Movies

Age (X) Spent (Y)

30 2.85

50 6.50

34 1.50

12 6.35

37 6.20

33 6.75

36 3.60

26 6.10

18 8.35

46 4.35

12.6 Number of Orders and Shipping Cost ($) ShipCost

Orders (X) Ship Cost (Y)

1,068 4,489

1,026 5,611

767 3,290

885 4,113

1,156 4,883

1,146 5,425

892 4,414

938 5,506

769 3,346

677 3,673

1,174 6,542

1,009 5,088

12.8 (a) Interpret the slope of the fitted regression Sales = 842 − 37.5 Price. (b) If Price = 20, what is

the prediction for Sales? (c) Would the intercept be meaningful if this regression represents DVD

sales at Blockbuster?

12.10 The regression equation NetIncome = 2,277 + .0307 Revenue was fitted from a sample of 100

leading world companies (variables are in millions of dollars). (a) Interpret the slope. (b) Is the intercept

meaningful? Explain. (c) Make a prediction of NetIncome when Revenue = 1,000. (Data are

from www.forbes.com and Forbes 172, no. 2 [July 21, 2003], pp. 108-110.) Global100

Chapter 13 (no p-values): Section Exercise # 2, 4 ,6

13.2 Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The

regression model was Y = total sales (thousands of dollars), X1 = display floor space (square

meters), X2 = competitors' advertising expenditures (thousands of dollars), X3 = advertised price

(dollars per unit). (a) Write the fitted regression equation. (b) Interpret each coefficient. (c) Would

the intercept seem to have meaning in this regression? (d) Make a prediction for Sales when

FloorSpace = 80, CompetingAds = 100, and Price = 1,200. Bikes

13.4 Refer to the ANOVA table for this regression. (a) State the degrees of freedom for the F test for

overall significance. (b) Use Appendix F to look up the critical value of F for α = .05. (c) Calculate

the F statistic. Is the regression significant overall? (d) Calculate R2 and R2

adj, showing your

formulas clearly. Bikes

Source d.f. SS MS

Regression 3 1,196,410 398,803

Error 26 379,332 14,590

Total 29 1,575,742

13.6 Observations are taken on sales of a certain mountain bike in 30 sporting goods stores. The

regression model was Y = total sales (thousands of dollars), X1 = display floor space (square

meters), X2 = competitors' advertising expenditures (thousands of dollars), X3 = advertised

price (dollars per unit), X4 = rebate rate (percent of retail price). (a) Calculate the t statistic for

each coefficient to test for β = 0. (b) Look up the critical value of Student's t in Appendix D for a

two-tailed test at α = .01. Which coefficients differ significantly from zero? (c) Use Excel to find

the p-value for each coefficient. Bikes

Predictor Coefficient SE

Intercept 1225.4 397.3

FloorSpace 11.522 1.330

CompetingAds −6.935 3.905

Price −0.14955 0.08927

See attached files.

#### Solution Summary

The solution provides step by step method for the calculation of Mean Square and common population variance from one-way and Two-way ANOVA. The solution also provides step by step method for the calculation of correlation coefficient and regression analysis. Formula for the calculation and Interpretations of the results are also included.