A student used multiple regression analysis to study how family spending ( y ) i
ID: 3264996 • Letter: A
Question
A student used multiple regression analysis to study how family spending (y) is influenced by income (x1),
family size (x2), and additions to savings (x3). The variables y, x1, and x3 are measured in thousands of dollars.
The following results were obtained.
ANOVA
df
SS
Regression
3
45.9634
Residual
11
2.6218
Total
Coefficients
Standard Error
Intercept
0.0136
x1
0.7992
0.074
x2
0.2280
0.190
x3
-0.5796
0.920
a.
Write out the estimated regression equation for the relationship between the variables.
b.
Compute R2. What can you say about the strength of this relationship?
c.
Carry out a test to determine whether y is significantly related to the independent variables. Use a .05 level of significance.
d.
Carry out a test to see if x3 and y are significantly related. Use a .05 level of significance. Briefly discuss.
ANOVA
df
SS
Regression
3
45.9634
Residual
11
2.6218
Total
Explanation / Answer
Anova
df
SS
MS
F
Regression
3
45.9634
15.32113
64.281
Residual
11
2.6218
0.238345
Total
14
48.5852
MS = SS / df
MS (Regression) = 45.9634/3 = 15.32113
MS (Residual) = 2.6218 / 11 = 0.23845
F = MS (Regression)/MS (Residual) = 15.32113/0.238345 = 64.281
Question a)
y^ = 0.0136 + 0.7992x1 + 0.2280x2 -0.5796x3
Question b)
R-square = SSR / SST = 45.9634 / 48.5852 = 0.9460
Answer: 0.9460
Question c)
Here calculated F is 64.281 and the critical value at 5% level of 3, 11 degrees of freedom (from F-table) we get it as 3.587.
The test statistics is greater than the critical value; we reject the null hypothesis. At 5% level of significance we can conclude that y is significantly related to the independent variables.
Question d)
For x3 the value of test statistics t is
t = -0.5796 / 0.920
= -0.63
The critical t for 14 degrees of freedom is given as (-/+) 2.145. The absolute value of test statistics is less the critical value (0.63 < 2.145); we fail to reject the null hypothesis.
At 5% level of significance we cannot conclude that x3 and y are significantly related.
Anova
df
SS
MS
F
Regression
3
45.9634
15.32113
64.281
Residual
11
2.6218
0.238345
Total
14
48.5852
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