Personal wealth tends to increase with age as older individuals Have had more opportunities to earn and invest than younger individuals. The following data were obtained from a random sample of eight individuals and record the total wealth (Y) and their Personal wealth tends to increase with age as older individuals current age (X). Person Total wealth(‘000s of dollars) Y Age (Years) X A 280 36 B 450 72 C 250 48 D 320 51 E 470 80 F 250 40 G 330 55 H 430 72 A part of the output of a regression analysis of Y against X using Excel is given below. SUMMARY OUTPUT Regression Statistic Multiple R 0.954704 R Square 0.91146 Adjusted R Square 0.896703 Standard Error 28.98954 Observation 8 df SS MS F Significant F Regression 1 51907.64 51907.64 Residual 6 5042.361 840.3936 Total 7 56950 Coefficient Standard error T Stat P-value Intercept 45.2159 39.8049 Age 5.3265 0.6777 State the estimated regression line and interpret the slope coefficient. What is the estimated total present wealth when a person is 50 years old? What is the value of the coefficient of determination ? Interpret it. Test whether there is a significant relationship between wealth and age at the 10% significant level. Perform the test using the following six steps. Step 1. Statement of hypothesis Step2. Standardized test statistic. Step3. Level of Significance Step4. Decision rule Step5. Calculation of test statistic Step6. Conclusion
Personal wealth tends to increase with age as older individuals
Have had more opportunities to earn and invest than younger individuals. The following data were obtained from a random sample of eight individuals and record the total wealth (Y) and their Personal wealth tends to increase with age as older individuals current age (X).
Person |
Total wealth(‘000s of dollars) Y |
Age (Years)
X |
|
A |
280 |
36 |
|
B |
450 |
72 |
|
C |
250 |
48 |
|
D |
320 |
51 |
|
E |
470 |
80 |
|
F |
250 |
40 |
|
G |
330 |
55 |
|
H |
430 |
72 |
|
A part of the output of a
SUMMARY OUTPUT
Regression Statistic |
|
Multiple R |
0.954704 |
R Square |
0.91146 |
Adjusted R Square |
0.896703 |
Standard Error |
28.98954 |
Observation |
8 |
df |
SS
|
MS
|
F |
Significant F |
|
Regression |
1 |
51907.64 |
51907.64 |
|
|
Residual |
6 |
5042.361 |
840.3936 |
|
|
Total |
7 |
56950 |
|
|
|
|
Coefficient |
Standard error |
T Stat |
P-value |
Intercept |
45.2159 |
39.8049 |
|
|
Age |
5.3265 |
0.6777 |
|
|
- State the estimated regression line and interpret the slope coefficient.
- What is the estimated total present wealth when a person is 50 years old?
- What is the value of the coefficient of determination ? Interpret it.
- Test whether there is a significant relationship between wealth and age at the 10% significant level. Perform the test using the following six steps.
Step 1. Statement of hypothesis
Step2. Standardized test statistic.
Step3. Level of Significance
Step4. Decision rule
Step5. Calculation of test statistic
Step6. Conclusion
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