Question

Question 2

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) 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 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

1. State the estimated regression line and interpret the slope coefficient.    (1.5 marks)
2. What is the estimated total personal wealth when a person is 50 years old?         (1 mark)
3. What is the value of the coefficient of determination? Interpret it.            (1.5 marks)
4. 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            (1 mark)

Step 2. Standardised test statistic    (0.5 mark)

Step 3. Level of significance (0.5 mark)

Step 4. Decision Rule (1.5 marks)

Step 5. Calculation of test statistic   (1.5 marks)

Step 6. Conclusion       (1 mark)

Answer 1

If ,t > 2.45 ,w we reject the null hypothesis.

5) test statistic , t = 7.86

6) since , t > 2.54 , we reject the null hypothesis. We can conclude that there exists r significant relationship between wealth and age.