Significance df SS MS F F Regression 2148222488 429644497.6 21.680 2.246E-14 Residual 94 1862816975 19817201.86 Total 99 4011039463 Standard Coefficients t Stat P-value Lower 95% Upper 95% Error Intercept 528.896 2512.847 0.210 0.8338 -4460,421 5518.213 Annual Income 2.936E- 139.220 15.531 8.964 108.382 170.058 ($1000) 14 Household Size 821.824 232.404 3.536 0.0006 360.381 1283.266 Education -1104.740 299.596 -3.687 0.0004 -1699,595 -509.885 TV Hours 20.638 27.201 0.759 0.4499 -33.371 74.646 Age -8.312 45.476 -0.183 0.8554 -98.607 81.982 Find the predicted annual charges for a 44-year old customer with an annual income of $65 (thousand), a household size of 5, 2 years of post- high school education, 32 hours of watching television per week.

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**Multiple Regression Output Summary**

---

For this question, use the following multiple regression output (which may differ from the output in other questions, even though the variables are the same).

**Summary Output:**

**Regression Statistics:**

- **Multiple R:** 0.732
- **R Square:** 0.536
- **Adjusted R Square:** 0.511
- **Standard Error:** 4451.652
- **Observations:** 100

**ANOVA**

[Details on ANOVA not provided in the image]

---

*Explanation:*

- **Multiple R** refers to the correlation coefficient representing the strength and direction of a linear relationship between the observed and predicted values.
  
- **R Square** indicates the proportion of variance in the dependent variable that can be explained by the independent variables.
  
- **Adjusted R Square** is a modified version of R Square that adjusts for the number of predictors and provides a more accurate measure when multiple variables are involved.
  
- **Standard Error** is an estimate of the standard deviation of the regression's residuals, providing insight into the precision of the predictions.
  
- **Observations** denote the number of data points used in the regression analysis.

- **ANOVA** stands for Analysis of Variance, a statistical method used to analyze differences among group means and their associated procedures.
Transcribed Image Text:**Multiple Regression Output Summary** --- For this question, use the following multiple regression output (which may differ from the output in other questions, even though the variables are the same). **Summary Output:** **Regression Statistics:** - **Multiple R:** 0.732 - **R Square:** 0.536 - **Adjusted R Square:** 0.511 - **Standard Error:** 4451.652 - **Observations:** 100 **ANOVA** [Details on ANOVA not provided in the image] --- *Explanation:* - **Multiple R** refers to the correlation coefficient representing the strength and direction of a linear relationship between the observed and predicted values. - **R Square** indicates the proportion of variance in the dependent variable that can be explained by the independent variables. - **Adjusted R Square** is a modified version of R Square that adjusts for the number of predictors and provides a more accurate measure when multiple variables are involved. - **Standard Error** is an estimate of the standard deviation of the regression's residuals, providing insight into the precision of the predictions. - **Observations** denote the number of data points used in the regression analysis. - **ANOVA** stands for Analysis of Variance, a statistical method used to analyze differences among group means and their associated procedures.
### Regression Analysis Summary

#### ANOVA Table

| Source      | df  | SS         | MS          | F      | Significance F   |
|-------------|-----|------------|-------------|--------|------------------|
| Regression  | 5   | 214,822,248 | 42,964,449.76 | 21.680 | 2.246E-14        |
| Residual    | 94  | 186,281,697 | 1,981,720.186|
| Total       | 99  | 401,103,946 |

#### Coefficients Table

| Predictor         | Coefficients | Standard Error | t Stat  | P-value  | Lower 95%  | Upper 95%  |
|-------------------|--------------|----------------|---------|----------|------------|------------|
| Intercept         | 528.896      | 2512.847       | 0.210   | 0.8338   | -4460.421  | 5518.213   |
| Annual Income ($1000) | 139.220      | 15.531         | 8.964   | 2.936E-14| 108.382    | 170.058    |
| Household Size    | 821.824      | 232.404        | 3.536   | 0.0006   | 360.381    | 1283.266   |
| Education         | -1104.740    | 299.596        | -3.687  | 0.0004   | -1699.595  | -509.885   |
| TV Hours          | 20.638       | 27.201         | 0.759   | 0.4499   | -33.371    | 74.646     |
| Age               | -8.312       | 45.476         | -0.183  | 0.8554   | -98.607    | 81.982     |

#### Problem Statement

Find the predicted annual charges for a 44-year-old customer with an annual income of $65,000, a household size of 5, 2 years of post-high school education, and 32 hours of watching television per week.
Transcribed Image Text:### Regression Analysis Summary #### ANOVA Table | Source | df | SS | MS | F | Significance F | |-------------|-----|------------|-------------|--------|------------------| | Regression | 5 | 214,822,248 | 42,964,449.76 | 21.680 | 2.246E-14 | | Residual | 94 | 186,281,697 | 1,981,720.186| | Total | 99 | 401,103,946 | #### Coefficients Table | Predictor | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |-------------------|--------------|----------------|---------|----------|------------|------------| | Intercept | 528.896 | 2512.847 | 0.210 | 0.8338 | -4460.421 | 5518.213 | | Annual Income ($1000) | 139.220 | 15.531 | 8.964 | 2.936E-14| 108.382 | 170.058 | | Household Size | 821.824 | 232.404 | 3.536 | 0.0006 | 360.381 | 1283.266 | | Education | -1104.740 | 299.596 | -3.687 | 0.0004 | -1699.595 | -509.885 | | TV Hours | 20.638 | 27.201 | 0.759 | 0.4499 | -33.371 | 74.646 | | Age | -8.312 | 45.476 | -0.183 | 0.8554 | -98.607 | 81.982 | #### Problem Statement Find the predicted annual charges for a 44-year-old customer with an annual income of $65,000, a household size of 5, 2 years of post-high school education, and 32 hours of watching television per week.
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