Regression Analysis and Super Grocery Stores

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Chap 13
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...
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