Find the equation of the regression 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 2 51 4 (a) x= 2 hours (c) x = 15 hours (b) x= 3.5 hours 38 45 47 65 67 (d) x=25 hours Find the regression equation. (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.)
Find the equation of the regression 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 2 51 4 (a) x= 2 hours (c) x = 15 hours (b) x= 3.5 hours 38 45 47 65 67 (d) x=25 hours Find the regression equation. (Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 2SGR
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![Find the equation of the regression 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, \( y \) |
| --- | --- |
| 1 | 38 |
| 1 | 45 |
| 2 | 51 |
| 4 | 47 |
| 4 | 65 |
| 5 | 67 |
Find the regression equation:
\[
\hat{y} = [ ]x + ([])
\]
(Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.)
Predict the values for:
- \( x = 2 \) hours
- \( x = 3.5 \) hours
- \( x = 15 \) hours
- \( x = 2.5 \) hours
### Explanation:
1. **Data Points**: Six data points are given, with \( x \) representing the hours spent studying and \( y \) representing the test score.
2. **Scatter Plot**: Plot the points on a graph with \( x \)-axis as the hours spent studying and \( y \)-axis as the test scores. Each point represents a student's study time and corresponding score.
3. **Regression Line**: Draw a line that best fits the data points on the scatter plot. This line is called the "line of best fit" or "regression line."
4. **Regression Equation**: The equation of the line will be of the form \( \hat{y} = mx + c \), where \( m \) is the slope and \( c \) is the y-intercept. Calculate these values using statistical methods to find the line of best fit.
5. **Predictions**: Use the regression equation to estimate test scores for the given additional study times.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3df97ab4-6262-4c33-b8aa-4d9fb25466b6%2F8a2bf53b-966a-478c-8630-697507f6c6de%2Fo99m6am_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the equation of the regression 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, \( y \) |
| --- | --- |
| 1 | 38 |
| 1 | 45 |
| 2 | 51 |
| 4 | 47 |
| 4 | 65 |
| 5 | 67 |
Find the regression equation:
\[
\hat{y} = [ ]x + ([])
\]
(Round the slope to three decimal places as needed. Round the y-intercept to two decimal places as needed.)
Predict the values for:
- \( x = 2 \) hours
- \( x = 3.5 \) hours
- \( x = 15 \) hours
- \( x = 2.5 \) hours
### Explanation:
1. **Data Points**: Six data points are given, with \( x \) representing the hours spent studying and \( y \) representing the test score.
2. **Scatter Plot**: Plot the points on a graph with \( x \)-axis as the hours spent studying and \( y \)-axis as the test scores. Each point represents a student's study time and corresponding score.
3. **Regression Line**: Draw a line that best fits the data points on the scatter plot. This line is called the "line of best fit" or "regression line."
4. **Regression Equation**: The equation of the line will be of the form \( \hat{y} = mx + c \), where \( m \) is the slope and \( c \) is the y-intercept. Calculate these values using statistical methods to find the line of best fit.
5. **Predictions**: Use the regression equation to estimate test scores for the given additional study times.
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