The answer to each of the following questions will be one of the points labeled A-H on the scatterplot. (i) Of the sales that received lower-than-predicted tips, which one had the lowest sale amount?                             [ Select ]                          ["D", "E", "A", "B", "F", "H", "G", "C"]            (ii) Which sale received the best tip, that is, which sale had the tip that was highest above the tip predicted for it?                             [ Select ]                          ["A", "B", "D", "E", "C", "G", "H", "F"]            (iii) Which data point has the smallest residual?                             [ Select ]                          ["A", "C", "F", "H", "D", "G", "B", "E"]            (iv) Of E and F, the model makes a better prediction for                             [ Select ]                          ["E", "F"]

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The answer to each of the following questions will be one of the points labeled A-H on the scatterplot.

(i) Of the sales that received lower-than-predicted tips, which one had the lowest sale amount?                             [ Select ]                          ["D", "E", "A", "B", "F", "H", "G", "C"]           

(ii) Which sale received the best tip, that is, which sale had the tip that was highest above the tip predicted for it?                             [ Select ]                          ["A", "B", "D", "E", "C", "G", "H", "F"]           

(iii) Which data point has the smallest residual?                             [ Select ]                          ["A", "C", "F", "H", "D", "G", "B", "E"]           

(iv) Of E and F, the model makes a better prediction for                             [ Select ]                          ["E", "F"]            .

### ANOVA Table

|             | df | SS          | MS          | F          | Significance F  |
|-------------|----|-------------|-------------|------------|-----------------|
| Regression  | 1  | 24360.81754 | 24360.81754 | 29.50102381 | 1.15405E-06     |
| Residual    | 58 | 47894.18246 | 825.7617666 |            |                 |
| Total       | 59 | 72255       |             |            |                 |

### Coefficients Table

|               | Coefficients  | Standard Error | t Stat      | P-value   | Lower 95%    | Upper 95%    |
|---------------|---------------|----------------|-------------|-----------|--------------|--------------|
| Intercept     | 56.95659334   | 12.27319518    | 4.640730674 | 2.02919E-05 | 32.38912416 | 81.52406252 |
| Sale Amount   | 0.126993685   | 0.023381027    | 5.431484494 | 1.15405E-06 | 0.080191475 | 0.173795894 |

---

**Explanation:**

The ANOVA table summarizes the variance in different components:

- **Regression**: Shows the variance attributed to the model (predictor variables) with a degrees of freedom (df) of 1.
  - **SS** (Sum of Squares) = 24360.81754
  - **MS** (Mean Squares) = 24360.81754
  - **F** (F-value) = 29.50102381
  - **Significance F**: p-value indicating the model's statistical significance.
  
- **Residual**: Represents variance that cannot be explained by the model with a df of 58.
  - **SS** = 47894.18246
  - **MS** = 825.7617666

- **Total**: Sum of total variance in the data with a df of 59.
  - **SS** = 72255

The **Coefficients table** provides details about the regression equation:

- **Intercept**: Coefficient of 56.95659334 with a standard error of 12
Transcribed Image Text:### ANOVA Table | | df | SS | MS | F | Significance F | |-------------|----|-------------|-------------|------------|-----------------| | Regression | 1 | 24360.81754 | 24360.81754 | 29.50102381 | 1.15405E-06 | | Residual | 58 | 47894.18246 | 825.7617666 | | | | Total | 59 | 72255 | | | | ### Coefficients Table | | Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |---------------|---------------|----------------|-------------|-----------|--------------|--------------| | Intercept | 56.95659334 | 12.27319518 | 4.640730674 | 2.02919E-05 | 32.38912416 | 81.52406252 | | Sale Amount | 0.126993685 | 0.023381027 | 5.431484494 | 1.15405E-06 | 0.080191475 | 0.173795894 | --- **Explanation:** The ANOVA table summarizes the variance in different components: - **Regression**: Shows the variance attributed to the model (predictor variables) with a degrees of freedom (df) of 1. - **SS** (Sum of Squares) = 24360.81754 - **MS** (Mean Squares) = 24360.81754 - **F** (F-value) = 29.50102381 - **Significance F**: p-value indicating the model's statistical significance. - **Residual**: Represents variance that cannot be explained by the model with a df of 58. - **SS** = 47894.18246 - **MS** = 825.7617666 - **Total**: Sum of total variance in the data with a df of 59. - **SS** = 72255 The **Coefficients table** provides details about the regression equation: - **Intercept**: Coefficient of 56.95659334 with a standard error of 12
The graph and the Excel summary output below are about the weekend sales and tips at a certain Sonny’s restaurant in Tallahassee, FL. Use them to answer the SONNY’S questions that follow.

The data was gathered by Sonny’s employee Joshua Gonzalez for his group project in my Summer 2007 STA 2122 class.

**SLRI SONNY’S SCATTERPLOT**

- **Graph Explanation:** The scatterplot represents the relationship between the sale amount ($) on the x-axis and the tip amount ($) on the y-axis. There is a trend line indicating a positive correlation between sales and tips. Data points such as A, B, C, D, E, F, G, and H represent different observations within this data set.

© 2020 Radha Bose Florida State University Department of Statistics

---

**SUMMARY OUTPUT**

**SONNY'S**

| Regression Statistics  |               |
|------------------------|---------------|
| Multiple R             | 0.58064672    |
| R Square               | 0.337150613   |
| Adjusted R Square      | 0.325722175   |
| Standard Error         | 28.73607083   |
| Observations           | 60            |

**Explanation:**

- **Multiple R:** This indicates the correlation coefficient, showing a moderate positive relationship between sales and tips.
- **R Square (R²):** Represents the proportion of the variance in the tip amount that can be predicted from the sale amount, roughly 33.7%.
- **Adjusted R Square:** Adjusts the R² value based on the number of predictors; in this case, it is slightly lower.
- **Standard Error:** Reflects the average distance that the observed values fall from the regression line.
- **Observations:** The total number of data points, which is 60.
Transcribed Image Text:The graph and the Excel summary output below are about the weekend sales and tips at a certain Sonny’s restaurant in Tallahassee, FL. Use them to answer the SONNY’S questions that follow. The data was gathered by Sonny’s employee Joshua Gonzalez for his group project in my Summer 2007 STA 2122 class. **SLRI SONNY’S SCATTERPLOT** - **Graph Explanation:** The scatterplot represents the relationship between the sale amount ($) on the x-axis and the tip amount ($) on the y-axis. There is a trend line indicating a positive correlation between sales and tips. Data points such as A, B, C, D, E, F, G, and H represent different observations within this data set. © 2020 Radha Bose Florida State University Department of Statistics --- **SUMMARY OUTPUT** **SONNY'S** | Regression Statistics | | |------------------------|---------------| | Multiple R | 0.58064672 | | R Square | 0.337150613 | | Adjusted R Square | 0.325722175 | | Standard Error | 28.73607083 | | Observations | 60 | **Explanation:** - **Multiple R:** This indicates the correlation coefficient, showing a moderate positive relationship between sales and tips. - **R Square (R²):** Represents the proportion of the variance in the tip amount that can be predicted from the sale amount, roughly 33.7%. - **Adjusted R Square:** Adjusts the R² value based on the number of predictors; in this case, it is slightly lower. - **Standard Error:** Reflects the average distance that the observed values fall from the regression line. - **Observations:** The total number of data points, which is 60.
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