Report an appropriate hypothesis test for a positive linear relationship and use a 5% significance level. Explain the potential error in words, in context. In the answer options below I have used the phrase “a certain relationship” because I don’t want to give away exactly what type of relationship it is. Group of answer choices We would be accepting that there was a certain relationship between Sale amount and Tip when actually there wasn’t. We would not be accepting that there was a certain relationship between Sale amount and Tip when indeed there wasn’t. We would not be accepting that there was a certain relationship between Sale amount and Tip when actually there was. We would be accepting that there was a certain relationship between Sale amount and Tip when indeed there was.

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Report an appropriate hypothesis test for a positive linear relationship and use a 5% significance level.

Explain the potential error in words, in context.

In the answer options below I have used the phrase “a certain relationship” because I don’t want to give away exactly what type of relationship it is.

Group of answer choices
We would be accepting that there was a certain relationship between Sale amount and Tip when actually there wasn’t.
We would not be accepting that there was a certain relationship between Sale amount and Tip when indeed there wasn’t.
We would not be accepting that there was a certain relationship between Sale amount and Tip when actually there was.
We would be accepting that there was a certain relationship between Sale amount and Tip when indeed there was.
### 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  |

- **Analysis of Variance (ANOVA)**: This section displays the variance breakdown for the regression analysis. It includes degrees of freedom (df), sum of squares (SS), mean square (MS), F-statistic, and significance F.

- **Regression**: Examines the effect of the independent variable (Sale Amount) on the dependent variable, focusing on variance due to the model.

- **Residual**: Represents variance not explained by the model.

- **Total**: Total variance in the data.

- **Coefficients Analysis**: Provides the regression coefficients for the intercept and the independent variable (Sale Amount), along with their standard error, t-statistic, p-value, and confidence intervals.

#### Source
© 2020 Radha Bose Florida State University Department of Statistics
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 | - **Analysis of Variance (ANOVA)**: This section displays the variance breakdown for the regression analysis. It includes degrees of freedom (df), sum of squares (SS), mean square (MS), F-statistic, and significance F. - **Regression**: Examines the effect of the independent variable (Sale Amount) on the dependent variable, focusing on variance due to the model. - **Residual**: Represents variance not explained by the model. - **Total**: Total variance in the data. - **Coefficients Analysis**: Provides the regression coefficients for the intercept and the independent variable (Sale Amount), along with their standard error, t-statistic, p-value, and confidence intervals. #### Source © 2020 Radha Bose Florida State University Department of Statistics
**Sales and Tips Analysis at Sonny's Restaurant**

The graph and the Excel summary output presented here illustrate the weekend sales and tips at a Sonny’s restaurant in Tallahassee, FL. This data can be used to address the accompanying questions.

**Data Collection**  
This data was collected by Sonny’s employee Joshua Gonzalez as part of a group project for his Summer 2007 STA 2122 class.

**Scatterplot Analysis**

The scatterplot visualizes the relationship between sale amounts and the corresponding tips at Sonny's restaurant. The x-axis represents the sale amount in dollars ($), while the y-axis denotes the tip amount in dollars ($). Several data points are plotted, showing a general trend that is encapsulated by a linear regression line. Specific points labeled A through H illustrate particular data instances:

- Each plotted point represents a unique sale-tip pair.
- The line indicates a positive correlation, suggesting higher sales are generally associated with higher tips.

**Summary Output**

The regression statistics from the analysis are as follows:

- **Multiple R**: 0.58064672, indicating the correlation coefficient between sales and tips.
- **R Square**: 0.337150613, showing that approximately 33.7% of the variance in tips can be explained by the sales data.
- **Adjusted R Square**: 0.325722175, providing a more adjusted view of the R Square metric, accounting for the number of predictors.
- **Standard Error**: 28.73607083, describing the average distance that the observed values fall from the regression line.
- **Observations**: 60, indicating the number of data points or sale-tip observations involved in the analysis.

This analysis is © 2020 by Radha Bose, Florida State University Department of Statistics.
Transcribed Image Text:**Sales and Tips Analysis at Sonny's Restaurant** The graph and the Excel summary output presented here illustrate the weekend sales and tips at a Sonny’s restaurant in Tallahassee, FL. This data can be used to address the accompanying questions. **Data Collection** This data was collected by Sonny’s employee Joshua Gonzalez as part of a group project for his Summer 2007 STA 2122 class. **Scatterplot Analysis** The scatterplot visualizes the relationship between sale amounts and the corresponding tips at Sonny's restaurant. The x-axis represents the sale amount in dollars ($), while the y-axis denotes the tip amount in dollars ($). Several data points are plotted, showing a general trend that is encapsulated by a linear regression line. Specific points labeled A through H illustrate particular data instances: - Each plotted point represents a unique sale-tip pair. - The line indicates a positive correlation, suggesting higher sales are generally associated with higher tips. **Summary Output** The regression statistics from the analysis are as follows: - **Multiple R**: 0.58064672, indicating the correlation coefficient between sales and tips. - **R Square**: 0.337150613, showing that approximately 33.7% of the variance in tips can be explained by the sales data. - **Adjusted R Square**: 0.325722175, providing a more adjusted view of the R Square metric, accounting for the number of predictors. - **Standard Error**: 28.73607083, describing the average distance that the observed values fall from the regression line. - **Observations**: 60, indicating the number of data points or sale-tip observations involved in the analysis. This analysis is © 2020 by Radha Bose, Florida State University Department of Statistics.
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