Personal wealth tends to increase with age as older individuals have had more opportunitiesto earn and invest than younger individuals. The following data were obtained from a randomsample of eight individuals and records their total wealth (Y) and their current age (X). See attachment for table with figures 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 The table below represents a dataset comparing the total wealth (in thousands of dollars) and age (in years) of six individuals labeled A to F.| 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 |In this table:- Column **Person** lists the individual labels A through F.- Column **Total wealth ('000s of dollars)** (labeled **Y**) indicates each person's total wealth in thousands of dollars.- Column **Age (Years)** (labeled **X**) shows the age of each individual in years. This dataset can be used to analyze the relationship between age and total wealth among these six individuals. **Regression Analysis of Y against X Using Excel**In this section, we provide an interpretation of a regression analysis output of variable Y against variable X using Microsoft Excel. The analysis includes key statistical measures and an ANOVA table.**Summary Output****Regression Statistics**- **Multiple R:** 0.954704 - This metric indicates the correlation coefficient between the observed and predicted values of Y. A value closer to 1 suggests a strong positive correlation.- **R Square:** 0.91146 - Represents the proportion of the variance in the dependent variable (Y) that is predictable from the independent variable (X). Approximately 91.15% of the variability in Y can be explained by X in this model.- **Adjusted R Square:** 0.896703 - This is the R Square value adjusted for the number of predictors in the model, reflecting the goodness-of-fit more accurately for models with multiple predictors.- **Standard Error:** 28.98954 - The average distance that the observed values fall from the regression line. Lower values imply a better fit.- **Observations:** 8 - Indicates the number of data points used for the analysis.**ANOVA (Analysis of Variance) Table**The ANOVA table breaks down the variance in the data into components attributable to different sources.| Source of Variation | df | SS | MS | F | Significance F ||---------------------|----|---------|-----------|----------|----------------|| Regression | 1 | 51907.64| 51907.64 | 61.73 | 1.2014E-03 || Residual | 6 | 5042.361| 840.3936 | | || Total | 7 | 56950 | | | |- **df:** Degrees of freedom - Regression: 1 - Residual: 6 - Total: 7- **SS (Sum of Squares):** - Regression: 51907.64 - Residual: 5042.361 - Total: 56950- **MS (Mean Square):** - Regression: 51907.64 - Residual: 840.3936- **F-Value:** 61.73

Answered: Personal wealth tends to increase with…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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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). See attachment for table with figures

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

The table below represents a dataset comparing the total wealth (in thousands of dollars) and age (in years) of six individuals labeled A to F.

| 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 |

In this table:
- Column **Person** lists the individual labels A through F.
- Column **Total wealth ('000s of dollars)** (labeled **Y**) indicates each person's total wealth in thousands of dollars.
- Column **Age (Years)** (labeled **X**) shows the age of each individual in years.

This dataset can be used to analyze the relationship between age and total wealth among these six individuals.

**Regression Analysis of Y against X Using Excel**

In this section, we provide an interpretation of a regression analysis output of variable Y against variable X using Microsoft Excel. The analysis includes key statistical measures and an ANOVA table.

**Summary Output**

**Regression Statistics**
- **Multiple R:** 0.954704
- This metric indicates the correlation coefficient between the observed and predicted values of Y. A value closer to 1 suggests a strong positive correlation.
- **R Square:** 0.91146
- Represents the proportion of the variance in the dependent variable (Y) that is predictable from the independent variable (X). Approximately 91.15% of the variability in Y can be explained by X in this model.
- **Adjusted R Square:** 0.896703
- This is the R Square value adjusted for the number of predictors in the model, reflecting the goodness-of-fit more accurately for models with multiple predictors.
- **Standard Error:** 28.98954
- The average distance that the observed values fall from the regression line. Lower values imply a better fit.
- **Observations:** 8
- Indicates the number of data points used for the analysis.

**ANOVA (Analysis of Variance) Table**

The ANOVA table breaks down the variance in the data into components attributable to different sources.

| Source of Variation | df | SS | MS | F | Significance F |
|---------------------|----|---------|-----------|----------|----------------|
| Regression | 1 | 51907.64| 51907.64 | 61.73 | 1.2014E-03 |
| Residual | 6 | 5042.361| 840.3936 | | |
| Total | 7 | 56950 | | | |

- **df:** Degrees of freedom
- Regression: 1
- Residual: 6
- Total: 7
- **SS (Sum of Squares):**
- Regression: 51907.64
- Residual: 5042.361
- Total: 56950
- **MS (Mean Square):**
- Regression: 51907.64
- Residual: 840.3936
- **F-Value:** 61.73

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