VIII. Regarding the data offered in problem VII, we are interested in identifying which is the best statistical relationship between the variables considered.
Using all the information previously obtained by you, I analyzed:
- the correlation coefficients, identifying which is the best
and the weakest among all the possible regressions and
equations.
- the regression errors obtained, identifying which is the best and
the weakest among all the possible regressions and equations.
- the required hypothesis tests
The before data was:
VII. Fran’s Convenience Marts is located throughout the Erie, Pennsylvania metro area. Fran, the owner, wants to expand her businesses to other communities in northwest Pennsylvania and southeast New York, such as Jamestown, Corry, Meadville, and Warren. To prepare your presentation to the local bank, you would like to better understand the factors that make a particular discount store productive. Fran must do all the work on her own, so she won't be able to study all the discount stores. Therefore, he selects a random sample of 15 stores and records the average daily sales, the floor space (area), the number of parking spaces and the average income of the families in the region for each of the stores. The sample information is reported below.
Stores |
Daily Sales |
Store Area |
Parking Space | Income (thousand of dollars) |
1 |
$1840 |
532 |
6 |
44 |
2 |
1746 |
478 |
4 |
51 |
3 |
1812 |
530 |
7 |
45 |
4 |
1806 |
508 |
7 |
46 |
5 |
1792 |
514 |
5 |
44 |
6 |
1825 |
556 |
6 |
46 |
7 |
1811 |
541 |
4 |
49 |
8 |
1803 |
513 |
6 |
52 |
9 |
1830 |
532 |
5 |
46 |
10 |
1827 |
537 |
5 |
46 |
11 |
1764 |
499 |
3 |
48 |
12 |
1825 |
510 |
8 |
47 |
13 |
1763 |
490 |
4 |
48 |
14 |
1846 |
516 |
8 |
45 |
15 |
1815 |
482 |
7 |
43 |
- Present and identify which is the best equation to predict the monthly average purchase volume, explain why it is the best equation.
- With the best estimated equation present the confidence
interval to predict the monthly average purchase volume, when the
Area of
the store is 585, the family income is 50,000 and the parking
number is 10.
As per data set given in the question:
STORE AREA= 585
FAMILY INCOME = 50
PARKING NUMBER =10
With 82% C.I we can say that Daily_Sales Will be 1893 for abv given point.
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