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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 records their total wealth (Y) and their current age (X).
Person Total wealth (‘000s of dollars) Age (Years)
Y 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 Statistics
Multiple R 0.954704
R Square 0.91146
Adjusted R Square 0.896703
Standard Error 28.98954
Observations 8
ANOVA
df SS MS F Significance F
Regression 1 51907.64 51907.64
Residual 6 5042.361 840.3936
Total 7 56950
Coefficients Standard Error t Stat P-value
Intercept 45.2159 39.8049
Age 5.3265 0.6777
a. State the estimated regression line and interpret the slope coefficient.
b. What is the estimated total personal wealth when a person is 50 years old?
c. What is the value of the coefficient of determination? Interpret it.
d. Test whether there is a significant relationship between wealth and age at the 10%significance level. Perform the test using the following six steps.
Step 1. Statement of the hypotheses
Step 2. Standardised test statistic
Step 3. Level of significance
Step 4. Decision Rule
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