An example may help to better understand the use of regression analysis.

A market researcher for Super Dollar Super Markets is studying the yearly amount families of four or more spend on food. Three independent variables are thought to be related to yearly food expenditures (Food). Those variables are: total family income (Income) in $00, size of family (Size), and whether the family has children in college (College).

The following is the data:

Family	Food	Income	Size	Student
1	3900	376	4	0
2	5300	515	5	1
3	4300	516	4	0
4	4900	468	5	0
5	6400	538	6	1
6	7300	626	7	1
7	4900	543	5	0
8	5300	437	4	0
9	6100	608	5	1
10	6400	513	6	1
11	7400	493	6	1
12	5800	563	5	0

The following is the regression analysis which can be performed with Excel:

The regression equation is

Food = 954 + 1.09 Income + 748 Size + 565 Student

Predictor Coef SE Coef T P

Constant 954 1581 0.60 0.563

Income 1.092 3.153 0.35 0.738

Size 748.4 303.0 2.47 0.039

Student 564.5 495.1 1.14 0.287

S = 572.7 R-Sq = 80.4% R-Sq(adj) = 73.1%

Analysis of Variance

Source DF SS MS F P

Regression 3 10762903 3587634 10.94 0.003

Residual Error 8 2623764 327970

Total 11 13386667

See the regression equation above:

Each additional $100 dollars of income per year will increase the amount spent on food by $109 per year.

An additional family member will increase the amount spent per year on food by $748.

A family with a college student will spend $565 more per year on food than those without a college student.

The regression equation provides use with the ability to predict the dependent variable food expenditures based on the independent variables such as income, family size and whether a student is in college or not. Linear regression helps us to understand the strength of the relationship between the variables and helps us to predict outcomes based on the regression equation. I would encourage you to try copying the data into an excel spreadsheet and use the data analysis or mega stat tools to perform a regression analysis and see if you come out with the same results I listed above. If anyone tries it, please share your experience with the class.

Thanks,

Dr. Hamel

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