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) Y 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. b. What is the estimated total personal wealth when a person is 50 years old? c. What is the value of the coefficient of determination? Interpret it. 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 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
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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) |
Age (Years) |
|
|
Y |
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. |
|
|
|
b. |
What is the estimated total personal wealth when a person is 50 years old? |
|
|
|
|
|
|
|
|
c. |
What is the value of the coefficient of determination? Interpret it. |
|
|
|
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 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
Solved in 4 steps with 3 images
