Question

MULTIPLE REGRESSION

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):

(f)   Are the results in line with Maslow’s hierarchy of needs? Explain.

Answer 1

Solution:

Part(a): Multiple regression model is,

here, Y is independent variable, is intercept , are slopes and x1,x2,x3 and x4 are independant variable.

Part(b): Estimated multiple regression model is,

Y=23.14156+0.5914 Income -0.3417 Rent -1.1197 Food -0.90787 Expense

Part (c): following are values estimated for intercept and slopes:

alpha (intercept)=23.14156

b1=0.5914

b2=-0.3417

b3=-1.1197

b4=-0.90787

Part(d): Weekly savings has significant linear relationship with variables weekly income, food and entertainment expenses.

Weekly savings has not linear relationship with rent.

Part (e): Weekly income, food and entertainment expenses there independent variables comes out be significant because p-values associated with these variables are less than 0.05 (significance level) therefore, we reject the null hypothesis that slope=0.

Independent variable rent is not significant because its p-value greater than level of significance alpha.