Researchers are investigating how the amount of monthly rainfall, measured in centimeters (cm), affects the monthly growth, in cm, of a certain plant. From a sample of data, the researchers created a least-squares regression line. Computer output is shown in the following table. Which of the following statements is an interpretation of the value 0.75 shown in the table?

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Researchers are investigating how the amount of monthly rainfall, measured in centimeters (cm), affects the monthly growth, in cm, of a certain plant. From a sample of data, the researchers created a least-squares regression line. Computer output is shown in the following table.

Which of the following statements is an interpretation of the value 0.75 shown in the table?

| Variable   | DF | Estimate | SE  | T    |
|------------|----|----------|-----|------|
| Intercept  | 1  | 0.75     | 0.350 | 2.14 |
| Rainfall   | 1  | 0.15     | 0.025 | 6.00 |

### Explanation:

This table presents the results of a statistical analysis, likely from a regression model. Each row corresponds to a different variable in the model.

- **Variable**: Lists the variables considered in the model. Here, the variables are "Intercept" and "Rainfall".
  
- **DF (Degrees of Freedom)**: Indicates the number of independent values or quantities that can vary in the analysis. Each variable here has 1 degree of freedom.
  
- **Estimate**: Represents the estimated coefficient for each variable. For instance, the estimate for the Intercept is 0.75, and for Rainfall, it's 0.15.
  
- **SE (Standard Error)**: Measures the accuracy with which a sample represents a population. It is the standard deviation of the sampling distribution of a statistic. The standard error for the Intercept is 0.350, and for Rainfall, it is 0.025.
  
- **T (T-value)**: A statistic that measures the size of the difference relative to the variation in your sample data. A larger T-value indicates a larger difference. The T-value for the Intercept is 2.14, whereas for Rainfall, it is 6.00, suggesting Rainfall has a stronger effect in the model compared to the Intercept.
Transcribed Image Text:| Variable | DF | Estimate | SE | T | |------------|----|----------|-----|------| | Intercept | 1 | 0.75 | 0.350 | 2.14 | | Rainfall | 1 | 0.15 | 0.025 | 6.00 | ### Explanation: This table presents the results of a statistical analysis, likely from a regression model. Each row corresponds to a different variable in the model. - **Variable**: Lists the variables considered in the model. Here, the variables are "Intercept" and "Rainfall". - **DF (Degrees of Freedom)**: Indicates the number of independent values or quantities that can vary in the analysis. Each variable here has 1 degree of freedom. - **Estimate**: Represents the estimated coefficient for each variable. For instance, the estimate for the Intercept is 0.75, and for Rainfall, it's 0.15. - **SE (Standard Error)**: Measures the accuracy with which a sample represents a population. It is the standard deviation of the sampling distribution of a statistic. The standard error for the Intercept is 0.350, and for Rainfall, it is 0.025. - **T (T-value)**: A statistic that measures the size of the difference relative to the variation in your sample data. A larger T-value indicates a larger difference. The T-value for the Intercept is 2.14, whereas for Rainfall, it is 6.00, suggesting Rainfall has a stronger effect in the model compared to the Intercept.
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