Mortgage payment Gender Income

Surname 1
Name
Instructor
Course
Date
REGRESSION ANALYSIS
a. Correlation matrix
Income Value Years of
education
Age Mortgage
payment
Gende
r
Income 1
Value 0.7196
5
1
Years of
education
0.1880
44
-
0.1437
2
1
Age 0.2425
55
0.2195
04
0.620857787 1
Mortgage
payment
0.1176
76
0.3605
72
-0.213125505 -
0.044
1
1
Gender -
0.2744
1
-
0.0073
-0.061944104 -
0.186
3
0.198942133 1
Table 1
As can be observed from the correlation matrix above, the independent variables do not show
any high level of correlation with each other hence there no chances of multicollinearity.
b. Regression equation
SUMMARY
OUTPUTRegression Statistics
Multiple R
0.8440539
85
R Square
0.7124271
29
Adjusted R
Square
0.6367500
58
Standard Error
0.6336786
2
Observations 25

Surname 2
ANOVA
df
SS MS
F
Significan
ce F
Regression 5
18.901
0
3.780
2
9.414042
032
0.000121
662
Residual 19 7.6294
0.401
5
Total 24
26.530
4
Coefficient
s
Std
Error t Stat P-value
Lower
95%
Upper
95%
Intercept
28.616149
61 3.2065
8.924
5
3.1833E-
08 21.9049
35.3273
8
Value
0.0316195
35 0.0052
6.055
0
7.99203E-
06 0.0207 0.04255
Years of
education
0.7081650
23 0.2602
2.721
6
0.013543
079 0.1636 1.25278
Age -0.056936 0.0341
-
1.670
4
0.111234
348 -0.1283 0.01441
Mortgage
payment
-
0.0005255
01 0.0014
-
0.383
2
0.705857
263 -0.0034 0.00235
Gender
-
0.5876508
3 0.2669
-
2.201
8
0.040237
91 -1.1463
-
0.02902
Table 2
Regression equation
Income=0.032 ( value ) +0.71 ( years of educ ) −0.06 ( age )−0.0005 ( mortgage payment )−0.59 ( gender ) +28.62
c. The value of R-squared is 0.71.This means that the independent variables are responsible
for 71% of the variation that occurs in the response variable (income).
d. Prediction for income
Income=0.032 ( value ) +0.71 ( years of educ ) −0.06 ( age )−0.0005 ( mortgage payment )−0.59 ( gender ) +28.62
Income=0.032 ( 275000 )+ 0.71 ( 13 ) −0.06 ( 48 )−0.0005 ( 375 )−0.59 ( 2 ) +28.62
Income=8800+9.23−2.88−0.1875−1.18+28.62
Income=$ 8,833.60
e. Test for the significance of the independent variables (global hypothesis)
Hypothesis

Surname 3
H0: βi = 0
H1: βi ≠ 0
Alpha = 0.01
It can be observed that the p-value for the slope of mortgage payment, gender, age and years of
education are greater than 0.01 (level of significance) hence they are not different from zero.
f. Test for independence of variables (individual hypothesis)
Hypothesis
H0: β1 = 0; β2 = 0; β3 = 0; β4 = 0; β5 = 0
H1: β1 ≠ 0; β2 ≠ 0; β3 ≠ 0; β4 ≠ 0; β5 ≠ 0
At 0.01 level of significance
From the regression results above, p-values for all independent variables except “value” are
greater than the level of significance (0.01) as can be observed from the regression table above.
Independent variable “value” has a p-value of 0.00. This means that it is the only significant
variable at 0.01 level of significant. Therefore all the independent variables are dropped except
“value”.
g. The new regression model
SUMMARY
OUTPUT
Regression Statistics
Multiple R
0.719650
159
R Square
0.517896
352
Adjusted R
Square
0.496935
324
Standard
Error
0.745724
119
Observations 25
ANOVA
df
SS MS
F
Significa
nce F
Regression 1 13.74 13.74
24.7075
834
5.016E-
05
Residual 23
12.790
4
0.5561
04