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.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Week 10 q2
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
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SUMMARY OUTPUT |
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Regression Statistics |
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Multiple R |
0.954704 |
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R Square |
0.91146 |
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Adjusted R Square |
0.896703 |
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Standard Error |
28.98954 |
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Observations |
8 |
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ANOVA |
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df |
SS |
MS |
F |
Significance F |
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Regression |
1 |
51907.64 |
51907.64 |
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Residual |
6 |
5042.361 |
840.3936 |
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Total |
7 |
56950 |
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Coefficients |
Standard Error |
t Stat |
P-value |
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Intercept |
45.2159 |
39.8049 |
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Age |
5.3265 |
0.6777 |
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- 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.
- 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
Step by step
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