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                                             State the estimated regression line and interpret the slope coefficient. What is the estimated total personal wealth when a person is 50 years old? What is the value of the coefficient of determination? Interpret it.

Question

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.
  2. What is the estimated total personal wealth when a person is 50 years old?
  3. What is the value of the coefficient of determination? Interpret it.
  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

Step 2. Standardised test statistic

Step 3. Level of significance

Step 4. Decision Rule

Step 5. Calculation of test statistic

Step 6. Conclusion

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