The date set below was collected from a random sample of 15 households on the following variables: (1) Weekly Income, (2) House Rent, (3) Food Expense, (4) Entertainment Expense, and (5) Weekly Savings.

Sampled Weekly House Food Entertain/ Weekly
Individual Income Rent Expense Expense Savings
Case 1 $250 85 95 25 20
Case 2 $190 75 90 10 0
Case 3 $420 140 120 40 50
Case 4 $340 120 130 0 40
Case 5 $280 110 100 30 15
Case 6 $310 80 125 25 25
Case 7 $520 150 140 55 80
Case 8 $440 175 155 45 0
Case 9 $360 90 85 20 95
Case 10 $385 105 135 35 30
Case 11 $205 80 105 0 5
Case 12 $265 65 95 15 15
Case 13 $195 50 80 10 20
Case 14 $250 90 100 25 0
Case 15 $480 140 160 45 45

A multiple regression was run with WEEKLY SAVINGS as the DEPENDENT VARIABLE and the rest as the INDEPENDENT VARIABLES.

SAVINGS = b + b INCOME + b RENT + b FOOD + b ENTERT

The resulting computer output is on the next page.

COMPUTER OUTPUT PART I

WEEKLY SAVINGS
REGRESSION FUNCTION & ANOVA FOR SAVINGS

SAVINGS = 23.14156 + 0.591446 INCOME - 0.341793 RENT
- 1.119734 FOOD - 0.907868 ENTERT

R-Squared = 0.917562
Adjusted R-Squared = 0.870454
Standard error of estimate = 10.9635
Number of cases used = 12

Analysis of Variance
p-value
Source SS df MS F Value Sig Prob
Regression 9364.86 4 2341.21 19.47795 0.000677
Residual 841.39 7 120.198
Total 10206.250 11

COMPUTER OUTPUT PART II

WEEKLY SAVINGS
REGRESSION COEFFICIENTS FOR SAVINGS

Two-Sided p-value
Variable Coefficient Std Error t Value Sig Prob
Constant 23.14156 18.34071 1.26176 0.247451
INCOME 0.59145 0.07388 8.00526 0.000091
RENT -0.34179 0.19849 -1.72199 0.128743 *
FOOD -1.11973 0.24633 -4.54565 0.002650
ENTERT -0.90787 0.32460 -2.79689 0.026643

* indicates that the variable is marked for leaving

Standard error of estimate = 10.9635
Durbin-Watson statistic = 1.683103

Use the above computer output to respond to the following questions:
The Model was:

(a) The multiple regression model is:
ANSWER

(b) What is the estimated multiple regression?
ANSWER

(c) What are the estimated values of b , b , b , b , and b ?
ANSWERS b = ?
b = ?
b = ?
b = ?
b = ?

(d) What relationship exists between (i) SAVINGS and INCOME?, SAVINGS and RENT?, SAVINGS and FOOD expense, SAVINGS and ENTERTAINMENT expense?
ANSWERS

(e) Which of the four independent (explaining) variables are (is) significant in the multiple regression and which ones are (is) not significant and why? (Use α = 0.05 level of significance). Use α = 0.05 level ANSWERS

The statistically significant explaining variables are (Use α = 0.05 level):

Those that are not significant (Use α = 0.05 level):