) WEInsurU is attempting to predict how long customers will live based on how lo
ID: 3238677 • Letter: #
Question
) WEInsurU is attempting to predict how long customers will live based on how long their parents and grandparents have lived. Here is the results of the excel analysis.
A
B
C
D
E
F
1
SUMMARY OUTPUT
2
3
Regression Statistics
4
Multiple R
0.8608
5
R Square
0.7411
6
Adjusted R Square
0.7301
7
Standard Error
2.66
8
Observations
100
9
10
ANOVA
11
df
SS
MS
F
Significance F
12
Regression
4
1930
482.38
67.97
0.00000
13
Residual
95
674
7.10
14
Total
99
2604
15
16
Coefficients
Standard Error
t Stat
P-Value
17
Intercept
3.24
5.42
0.60
0.5512
18
Mother
0.451
0.0545
8.27
0.0000
19
Father
0.411
0.0498
8.26
0.0000
20
Gmother(s)
0.0166
0.0661
0.25
0.8028
21
Gfather(s)
0.0869
0.0657
1.32
0.1890
a. (7) What is the regression equation?
b. (5) What does the significance level of 0.00000 for F mean?
c. (4) Why is the adjusted R-square lower than the R-square? Explain.
d. (5) Which, if any, of the coefficients are statistically significant? How do you know?
e. (4) If an individual’s mother lived to be 86, their father lived to be 73, and grandmothers averaged 77 and the grandfathers lived to be 68 when they died. How long would you expect this individual to live?
A
B
C
D
E
F
1
SUMMARY OUTPUT
2
3
Regression Statistics
4
Multiple R
0.8608
5
R Square
0.7411
6
Adjusted R Square
0.7301
7
Standard Error
2.66
8
Observations
100
9
10
ANOVA
11
df
SS
MS
F
Significance F
12
Regression
4
1930
482.38
67.97
0.00000
13
Residual
95
674
7.10
14
Total
99
2604
15
16
Coefficients
Standard Error
t Stat
P-Value
17
Intercept
3.24
5.42
0.60
0.5512
18
Mother
0.451
0.0545
8.27
0.0000
19
Father
0.411
0.0498
8.26
0.0000
20
Gmother(s)
0.0166
0.0661
0.25
0.8028
21
Gfather(s)
0.0869
0.0657
1.32
0.1890
Explanation / Answer
a) Regression equation:
y = 3.24 + 0.451 (Mother) + 0.411 (Father) + 0.0166 (Gmothers) + 0.0869 (Gfathers)
b) significance level of 0.00000 for F represents the p - value for the ANOVA test and p - value close to 0 means we reject the null hypothesis Ho and hence,
The model is a good predictor of the dependent variable.
c) Adjusted R - square is lower than R - square because in adjusted R - square, we make adjustments on the basis of degrees of freedom. R - square gives the percentage of explained variation as if all independent variables in the model affect the dependent variable, whereas the adjusted R-squared gives the percentage of variation explained by only those independent variables that in reality affect the dependent variable.
d) If we see the p - values corresponding to the factors month, father, Gmother(s) and Gfather(s), we can observe that the p - values corresponding to Gmother(s) and Gfather(s) is very high which is making them insignificant variables in the prediction of dependent variable. Hence,
Only significant variables are mother and father.
e) For mother = 86, father = 73, gmother(s) = 77 and gfather(s) = 68,
y = 3.24 + 0.451 (86) + 0.411 (73) + 0.0166 (77) + 0.0869 (68)
y = 71
Hence,
The individual is expected to live for 71 years.
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