A professor wants to conduct a study in a statistics class to measure the effect of solving problems at home on the performance on the final exam. She collected data at random for 20 students from a class on the number of hours spent in a week doing problem sets at home (X) and their score on the final exam (Y), as shown in the following table. Answer questions (a) through (d) based on this data. X = # of hrs/week Y = score on the final 100 72 90 63 59 90 98 89 86 73 85 66 86 64 96 73 94 85 85 70 24 10 20 6 5 21 23 18 19 12 16 6 19 5 22 12 20 15 18 10 a. The regression slope is and the vertical intercept is b. The predicted final score of a student who studies for 12 hours every week is c. The coefficients of determination is and coefficient of non-determination is d. Perform an F-test for the significance of the regression at 0.05 level of significance. Answer if you found the model to be "significant" or "not significant" based on this test.

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# Study on the Effect of Problem Solving at Home on Final Exam Performance

A professor wants to conduct a study in a statistics class to measure the effect of solving problems at home on the performance on the final exam. She collected data at random for 20 students from a class on the number of hours spent in a week doing problem sets at home (X) and their score on the final exam (Y), as shown in the following table. Answer questions (a) through (d) based on this data.

| X = # of hrs/week | 24 | 10 | 20 | 6  | 5  | 21 | 23 | 18 | 19 | 12 | 16 | 6  | 19 | 5  | 22 | 12 | 20 | 15 | 18 | 10 |
|------------------|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|
| Y = score on the final | 100 | 72 | 90 | 63 | 59 | 90 | 98 | 89 | 86 | 73 | 85 | 66 | 86 | 64 | 96 | 73 | 94 | 85 | 85 | 70 |

### Questions

a. The regression slope is **[   ]** and the vertical intercept is **[   ]**.

b. The predicted final score of a student who studies for 12 hours every week is **[   ]**.

c. The coefficient of determination is **[   ]** and the coefficient of non-determination is **[   ]**.

d. Perform an F-test for the significance of the regression at a 0.05 level of significance. Answer if you found the model to be "significant" or "not significant" based on this test.
   - **[   ]**

### Explanation of Graphs or Diagrams

This data can be visualized through a scatter plot with a regression line that represents the relationship between the number of study hours per week and the final exam scores. On the x-axis, we have the number of hours per week (X), while the y-axis represents the scores on the final exam (Y).

- **Scatter Plot**: Each point on the scatter plot represents a
Transcribed Image Text:# Study on the Effect of Problem Solving at Home on Final Exam Performance A professor wants to conduct a study in a statistics class to measure the effect of solving problems at home on the performance on the final exam. She collected data at random for 20 students from a class on the number of hours spent in a week doing problem sets at home (X) and their score on the final exam (Y), as shown in the following table. Answer questions (a) through (d) based on this data. | X = # of hrs/week | 24 | 10 | 20 | 6 | 5 | 21 | 23 | 18 | 19 | 12 | 16 | 6 | 19 | 5 | 22 | 12 | 20 | 15 | 18 | 10 | |------------------|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----| | Y = score on the final | 100 | 72 | 90 | 63 | 59 | 90 | 98 | 89 | 86 | 73 | 85 | 66 | 86 | 64 | 96 | 73 | 94 | 85 | 85 | 70 | ### Questions a. The regression slope is **[ ]** and the vertical intercept is **[ ]**. b. The predicted final score of a student who studies for 12 hours every week is **[ ]**. c. The coefficient of determination is **[ ]** and the coefficient of non-determination is **[ ]**. d. Perform an F-test for the significance of the regression at a 0.05 level of significance. Answer if you found the model to be "significant" or "not significant" based on this test. - **[ ]** ### Explanation of Graphs or Diagrams This data can be visualized through a scatter plot with a regression line that represents the relationship between the number of study hours per week and the final exam scores. On the x-axis, we have the number of hours per week (X), while the y-axis represents the scores on the final exam (Y). - **Scatter Plot**: Each point on the scatter plot represents a
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