EQuestion Help Find the equation of the tregression line for the given data. Then construct a scatter plot of the data and draw the regression line. (The pair of variables have a significant correlation) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. The number of hours 6 students spent for a test and their scores on that test are shown below. Hours spent studying, x Test score, y 3 47 (b) x = 25 hours (a) x= 2 hours (c) x= 12 hours 38 44 50 61 68 (d) x = 4 5 hours Find the regression equation. y = 6.269 x + (32.48 (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.) %3D Choose the correct graph below. OD. O A. OB. OB. Oc. 0- 80 80- Q Hours studying Hours studying Hours studying Hours studying 1012 (R.) Click to select your answer(s).

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**Title: Analyzing the Relationship Between Study Hours and Test Scores**

**Description:**

This exercise involves finding the equation of the regression line for the given data. You will construct a scatter plot and draw the regression line to explore the significant correlation between variables. The aim is to predict the test scores based on hours spent studying.

**Data Table: Hours vs. Test Scores**

| Hours spent studying, x | Test score, y |
|-------------------------|---------------|
| 2                       | 38            |
| 2.5                     | 44            |
| 3                       | 50            |
| 5                       | 47            |
| 5                       | 61            |
| 6                       | 68            |

**Tasks:**

1. **Find the regression equation**:
   - Regression equation: \( \hat{y} = 6.269x + 32.48 \)
   - The slope (rounded to three decimal places) is 6.269.
   - The y-intercept (rounded to two decimal places) is 32.48.

2. **Choose the correct graph**:
   - Four graph options (A, B, C, D) are provided to visualize the data and regression line.

**Graph Analysis:**

- The graphs display test scores vs. hours spent studying.
- A correct graph would show a scatter plot aligning with the calculated regression line, demonstrating the positive correlation between study time and scores.

Users are instructed to select the graph that correctly represents the data and regression analysis. 

**Predictive Use:**

Use this regression equation to predict test scores for different study durations:

- (a) \(x = 2\) hours
- (b) \(x = 2.5\) hours
- (c) \(x = 12\) hours
- (d) \(x = 4.5\) hours

**Instructions:**

Click to select your answer(s) based on the correct graphical representation of the regression analysis.
Transcribed Image Text:**Title: Analyzing the Relationship Between Study Hours and Test Scores** **Description:** This exercise involves finding the equation of the regression line for the given data. You will construct a scatter plot and draw the regression line to explore the significant correlation between variables. The aim is to predict the test scores based on hours spent studying. **Data Table: Hours vs. Test Scores** | Hours spent studying, x | Test score, y | |-------------------------|---------------| | 2 | 38 | | 2.5 | 44 | | 3 | 50 | | 5 | 47 | | 5 | 61 | | 6 | 68 | **Tasks:** 1. **Find the regression equation**: - Regression equation: \( \hat{y} = 6.269x + 32.48 \) - The slope (rounded to three decimal places) is 6.269. - The y-intercept (rounded to two decimal places) is 32.48. 2. **Choose the correct graph**: - Four graph options (A, B, C, D) are provided to visualize the data and regression line. **Graph Analysis:** - The graphs display test scores vs. hours spent studying. - A correct graph would show a scatter plot aligning with the calculated regression line, demonstrating the positive correlation between study time and scores. Users are instructed to select the graph that correctly represents the data and regression analysis. **Predictive Use:** Use this regression equation to predict test scores for different study durations: - (a) \(x = 2\) hours - (b) \(x = 2.5\) hours - (c) \(x = 12\) hours - (d) \(x = 4.5\) hours **Instructions:** Click to select your answer(s) based on the correct graphical representation of the regression analysis.
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