Researchers are wondering whether they can predict college GPA with the number of hours studying per week. To test this, they randomly select 8 college students, record their GPA and the number of hours spent studying per week. ID GPA 1 2.5 2 2.7 3 3.4 4 3.7 5 2.7 6 1.9 7 2.0 8 4.0 Hours studying per week 25.0 27.6 30.2 35.0 31.6 25.6 30.0 40.0 Based on the information in the table above, the researchers compute the regression equation: Y = -0.970+ 0.125 X. Do the researchers have enough evidence to claim that the number of hours studying predicts students' GPA? Select the null hypothesis for the statistical test: Ob=0 B=0 B = -0.970 b = 0.125
Researchers are wondering whether they can predict college GPA with the number of hours studying per week. To test this, they randomly select 8 college students, record their GPA and the number of hours spent studying per week. ID GPA 1 2.5 2 2.7 3 3.4 4 3.7 5 2.7 6 1.9 7 2.0 8 4.0 Hours studying per week 25.0 27.6 30.2 35.0 31.6 25.6 30.0 40.0 Based on the information in the table above, the researchers compute the regression equation: Y = -0.970+ 0.125 X. Do the researchers have enough evidence to claim that the number of hours studying predicts students' GPA? Select the null hypothesis for the statistical test: Ob=0 B=0 B = -0.970 b = 0.125
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![**Predicting GPA from Hours Studying: A Regression Analysis**
Researchers are investigating whether the number of hours spent studying per week can predict college GPA. To test this hypothesis, they randomly selected 8 college students, recorded their GPA and the number of hours spent studying per week. The data is summarized in the table below:
| ID | GPA | Hours studying per week |
|----|-----|-------------------------|
| 1 | 2.5 | 25.0 |
| 2 | 2.7 | 27.6 |
| 3 | 3.4 | 30.2 |
| 4 | 3.7 | 35.0 |
| 5 | 2.7 | 31.6 |
| 6 | 1.9 | 25.6 |
| 7 | 2.0 | 30.0 |
| 8 | 4.0 | 40.0 |
Based on the information in the table, the researchers computed the regression equation:
\[ \hat{Y} = -0.970 + 0.125X \]
where \( \hat{Y} \) represents the predicted GPA and \( X \) represents the hours spent studying per week.
### Research Question
Do the researchers have enough evidence to claim that the number of hours studying predicts students’ GPA?
### Statistical Test
Select the null hypothesis for the statistical test:
- \( b = 0 \)
- \( \beta = 0 \)
- \( \beta = -0.970 \)
- \( b = 0.125 \)
**Explanation of Regression Equation:**
The regression equation provided can be interpreted as follows:
- The coefficient \( 0.125 \) indicates that for each additional hour spent studying per week, the GPA is predicted to increase by 0.125, on average.
- The constant term \( -0.970 \) represents the y-intercept, which is the predicted GPA when the number of hours studying per week is zero.
**Null Hypothesis:**
To determine if the number of hours studying is a predictor of GPA, the null hypothesis \( \beta = 0 \) must be tested. This hypothesis states that the slope of the regression line is zero, meaning that there is no linear relationship between the number of hours studying and GPA. If this hypothesis is rejected](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf10b40a-fae6-4e8b-9b89-0711a68556bc%2Fe3d7b24a-7ec1-420d-82c0-41bbb6c64fed%2F3ea2hdm_processed.png&w=3840&q=75)
Transcribed Image Text:**Predicting GPA from Hours Studying: A Regression Analysis**
Researchers are investigating whether the number of hours spent studying per week can predict college GPA. To test this hypothesis, they randomly selected 8 college students, recorded their GPA and the number of hours spent studying per week. The data is summarized in the table below:
| ID | GPA | Hours studying per week |
|----|-----|-------------------------|
| 1 | 2.5 | 25.0 |
| 2 | 2.7 | 27.6 |
| 3 | 3.4 | 30.2 |
| 4 | 3.7 | 35.0 |
| 5 | 2.7 | 31.6 |
| 6 | 1.9 | 25.6 |
| 7 | 2.0 | 30.0 |
| 8 | 4.0 | 40.0 |
Based on the information in the table, the researchers computed the regression equation:
\[ \hat{Y} = -0.970 + 0.125X \]
where \( \hat{Y} \) represents the predicted GPA and \( X \) represents the hours spent studying per week.
### Research Question
Do the researchers have enough evidence to claim that the number of hours studying predicts students’ GPA?
### Statistical Test
Select the null hypothesis for the statistical test:
- \( b = 0 \)
- \( \beta = 0 \)
- \( \beta = -0.970 \)
- \( b = 0.125 \)
**Explanation of Regression Equation:**
The regression equation provided can be interpreted as follows:
- The coefficient \( 0.125 \) indicates that for each additional hour spent studying per week, the GPA is predicted to increase by 0.125, on average.
- The constant term \( -0.970 \) represents the y-intercept, which is the predicted GPA when the number of hours studying per week is zero.
**Null Hypothesis:**
To determine if the number of hours studying is a predictor of GPA, the null hypothesis \( \beta = 0 \) must be tested. This hypothesis states that the slope of the regression line is zero, meaning that there is no linear relationship between the number of hours studying and GPA. If this hypothesis is rejected
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