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.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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
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