Week 10 Question 2 (10 marks) 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 a State the estimated regression line and interpret the slope coefficient (1 5 marks) b What is the estimated total personal wealth when a person is 50 years old (1 mark) c What is the value of the coefficient of determination Interpret it (1 5 marks) 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 obtained from a random sample of eight individuals and records their total wealth (Y) and their current age (X) Perso Total wealth ('000s of Age n dollars) (Years) Y X A 280 36 B 450 72 O 250 48 D 320 51 m 470 80 F 250 40 HOLMES INSTITUTE Cum Progrin Suh Als Vol G 330 55 H 430 72

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Question: Week 10 Question 2 (10 marks) Personal wealth tends to increase with age as older individuals have had more opportunities to earn and invest than

Week 10

Question 2 (10 marks)

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)

280

450

250

320

470

250

330

430

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

ANOVA

Significance F

Regression

51907.64

Residual

5042.361

840.3936

Total

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.(1.5 marks)

b.What is the estimated total personal wealth when a person is 50 years old?(1 mark)

c.What is the value of the coefficient of determination? Interpret it.(1.5 marks)

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

Week 10 Question 2 (10 marks) Personal wealth tends to increase with

obtained from a random sample of eight individuals and records their total wealth (Y) and their current age (X). Perso Total wealth ('000s of Age n dollars) (Years) Y X A 280 36 B 450 72 O 250 48 D 320 51 m 470 80 F 250 40 HOLMES INSTITUTE Cum Progrin Suh Als Vol G 330 55 H 430 72

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