44

1.41001.3110

1.3 110 0.885

1.2 105 1.2105

1.1 120 0.975

1.4 80 1.170

1.0 105 1.195

A sample of 12 homes sold last week in St. Paul, Minnesota, is selected. Can we conclude that, as the size of the home (reported below in thousands of square feet) increases, the selling price (reported in $ thousands) also increases?

* Compute the coefficient of correlation.

* = [12(1344) – (13.8)(1160)]/12(16.26) – (13.8)2][12(114850) – (1160)2]=0.30722 * Determine the coefficient of determination

* r2 = 256.4103/2716.667=0.09438

* df = 12 -2 = 10

* table b2 t = 1.812; Reject the H0 if t > 1.812

* t = r ((n – 2)1/2) / (1 – r2)1/2 = (0.307220(10))1/2/(1-0.094384)1/2 = 0.9715/0.951663 = 1.028 * Accept H0. There is no relationship between the size of the home and the selling price.

58

A dog trainer is exploring the relationship between the size of the dog (weight in pounds) and its daily food consumption (measured in standard cups). Below is the result of a sample of 18 observations.

1 41 3

2 148 8

3 79 5

4 41 4

5 85 5

6 111 6

7 37 3

8 111 6

9 41 3

10 91 5

11 109 6

12 207 10

13 49 3

14 113 6

15 84 5

16 95 5

17 57 4

18 168 9

* Compute the correlation coefficient. Is it reasonable to conclude that the correlation in the population is greater than zero? Use the .05 significance level * r = [18(10496) – (1667)(96)]/ [18(192159) – (1667)2][18(582) – (96)2]=0.987 * Y = -29.7 + 22.93x

* Approximately 25 lb weight change

* Dog 12 is overeating

Chapter 14

Fran’s Convenience Marts are located throughout metropolitan Erie, Pennsylvania. Fran, the owner, would like to expand into other communities in northwestern Pennsylvania and southwestern New York, such as Jamestown, Corry, Meadville, and Warren. To prepare her presentation to the local bank, she would like to better understand the factors that make a particular outlet profitable. She must do all the work herself, so she will not be able to study all her outlets. She selects a random sample of 15 marts and records the average daily sales (Y), the floor space (area), the number of parking spaces, and the median income of families in that ZIP code region for each. The sample information is reported below

1$1,840532644

21,746478451

31,812530745

41,806508746

51,792514544

61,825556646

71,811541449

81,803513652

91,830532546

101,827537546

111,764499348

121,825510847

131,763490448

141,846516845

151,815482743

a. Determine the regression equation.

Y = 1480.74 + 0.731xs + 9.99xp - 2.30xi

b. What is the value of R2? Comment on the values?

R2 = 0.835 .

c. Conduct a global hypothesis test to determine if any of the independent variables are different from zero. Ho: B1=B2=B3=0

H1: Not all the B’s are 0

Reject if F is greater than 3.59

F = MSR/MSE

(10057.68/3)/(1982.32/11)=3352.56/180.21=18.60 Reject Null Hypothesis

d. Conduct individual hypothesis tests to determine if any of the independent variables can be dropped.

Store area

H0:B1=0

H1:B1≠0

Spaces

H0:B2=0

H1:B2≠0

Income

H0:B3=0

H1:B3≠0

df = 11 two tail test

t = 2.201

H0 is rejected if t < -2.201 or > 2.201

t = b1 – 0/Sb1

Store Area

t = 0.731 – 0 / 0.163 = 4.484

Parking Spaces

t = 9.991 - 0 / 2,599 = 3.844

Income

t = - 2.308 – 0 / 1.594 = -1.448

H0 is accepted for the income coefficient the income coefficient can be dropped

e. If variables are dropped, re-compute the regression equation and R2.

Y = 1342.5 + 0.772xs + 11.63xp

R2 = SSR/SS Total = 9680/12040 = 0.804

28

Many regions along the coast in North and South Carolina and Georgia have experienced rapid population...