Multiple regression analysis was used to study how an individual\'s income ( y i
ID: 357733 • Letter: M
Question
Multiple regression analysis was used to study how an individual's income (y in thousands of dollars) is influenced by age (X1 in years), level of education (X2 ranging from 1 to 5), and the individual's gender (X3 where 0 = female and 1 = male). The following is a partial result of a computer program that was used on a sample of 20 individuals.
Coefficients
Standard Error
X1
0.625
0.094
X2
0.921
0.190
X3
-0.510
0.920
ANOVA
df
SS
MS
F
Regression
_____
84
_____
_____
Error
_____
112
_____
Total
______
____
a) Write the regression equation for the above analysis. (4 Points)
b) Compute the multiple coefficient of determination (6 Points)
c) At the 5% level of significance, test to determine if the model is significant (i.e., perform an F test). (4 Points)
d) As you may note, the coefficient of X3 is -0.510. Interpret the meaning of this coefficient. (4 Points)
e) Based on the regression equation, what is the estimate of the mean income (in dollars) for a male individual who is 40 years old with an education level of 4. (4 Points)
Coefficients
Standard Error
X1
0.625
0.094
X2
0.921
0.190
X3
-0.510
0.920
ANOVA
df
SS
MS
F
Regression
_____
84
_____
_____
Error
_____
112
_____
Total
______
____
Explanation / Answer
a)regression equation : individual income Y =0.625X1+0.921X2-0.510X3
b)multiple coefficient of determination =SSR/SST =84/(112+84)=0.4286
c)
as p vlaue is significnatly lower then 0.05 ; the model is significant
d) this means that for if a person is male his income will be 0.510 less then female.
e) for above information income lavel = (0.625*40+0.921*4-0.510*1)*1000 =$ 28174
df SS MS F P value Regression 2 84 42 21.38 0.0000 Error 57 112 1.96491 Total 59 196Related Questions
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