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# Regression analysis

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3. The director of marketing at Reeves Wholesale Products is studying the monthly sales. Three independent variables were selected as estimators of sales: regional population, per-capita income and regional unemployment rate. The regression equation was computed to be (in pounds).

Y' = 64,100 + 0.394X1 + 9.6X2 + 11,600X3

a) What is the full name of the equation?
b) Interpret the number 64,100.
c) What are the estimated monthly sales for a particular region with a population of 796,000, per-capita income of £6,940 and an unemployment rate of 6.0%?

4. A sample of widowed senior citizens was studied to determine their degree of satisfaction with their present life. A special index, called the index of satisfaction, was used to measure satisfaction. Six factors were studied, namely, age at the time of first marriage (X1), annual income (X2), number of children living (X3), value of all assets (X4), status of health in the form of an index (X5) and the average number of social activities per week - such as bowling and dancing (X6). Suppose the multiple regression equation is:

Y' = 16.24 + 0.017X1 + 0.0028X2 + 42X3 + 0.0012X4 + 0.19X5 + 26.8X6

a) What is the estimated index of satisfaction for a person who first married at
18, has an annual income of £26,500, has 3 children living, has assets of £156,000, has an index of health status of 141 and has 2.5 social activities a week on the average?
b) Which would add more to satisfaction, an additional income of £10,000 a
year or 2 more social activities a week?

5. Refer to the following ANOVA table.

SOURCE DF SS MS F

Regression
3
21
7.0
2.33
Error 15 45 3.0
TOTAL 18 66

a) How large was the sample?
b) How many independent variables are there?
c) Compute the coefficient of multiple determination.
d) Compute the multiple standard error of estimate.

6. Refer to the following information

Predictor Coef StDev
Constant 20.00 10.00
X1 -1.00 0.25
X2 12.00 8.00
X1 -15.00 5.00

SOURCE DF SS MS F
Regression 3 7,500.00
Error 18
Total 21 10,000.00

a) Complete the ANOVA table.
b) Conduct a global test of hypothesis, using the 0.05 significance level. Can we conclude that any of the net regression coefficients are different from zero?
c) Conduct a test of hypothesis on each of the regression coefficients. Could you delete any of the variables?

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#### Solution Summary

Step by step method for regression analysis is discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution.

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