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The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, ỹ = bo + b¡x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statisticall significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 0. 1.5 3. 4 4.5 5.5 Overall Grades 87 86 79 78 76 67 65 Table Copy Data Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

The table below gives the number of hours spent unsupervised each day as well as the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, ỹ = bo + b¡x, for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statisticall significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Hours Unsupervised 0. 1.5 3. 4 4.5 5.5 Overall Grades 87 86 79 78 76 67 65 Table Copy Data Step 6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Understanding Regression Analysis: A Practical Example** The table below provides data on the number of hours spent unsupervised each day and the corresponding overall grade averages for seven middle school students. Using this data, you can explore the concept of a regression line, represented by the equation: \[ \hat{y} = b_0 + b_1x \] This equation is used to predict the overall grade average based on the number of unsupervised hours each day. **Data:** | Hours Unsupervised | Overall Grades | |--------------------|----------------| | 0 | 87 | | 1 | 86 | | 1.5 | 79 | | 3 | 78 | | 4 | 76 | | 4.5 | 67 | | 5.5 | 65 | **Note:** Keep in mind, the correlation coefficient may not be statistically significant. It’s important not to rely on the regression line for predictions if the correlation is not significant. **Task:** *Step 6 of 6:* Calculate the coefficient of determination (\(R^2\)), and round your answer to three decimal places. **Answer:** Provide your answer in the input box provided. This example illustrates how regression analysis can help understand potential relationships between variables, such as time spent unsupervised and academic performance. However, remember to assess the significance of the correlation before making predictions.
Transcribed Image Text:**Understanding Regression Analysis: A Practical Example** The table below provides data on the number of hours spent unsupervised each day and the corresponding overall grade averages for seven middle school students. Using this data, you can explore the concept of a regression line, represented by the equation: \[ \hat{y} = b_0 + b_1x \] This equation is used to predict the overall grade average based on the number of unsupervised hours each day. **Data:** | Hours Unsupervised | Overall Grades | |--------------------|----------------| | 0 | 87 | | 1 | 86 | | 1.5 | 79 | | 3 | 78 | | 4 | 76 | | 4.5 | 67 | | 5.5 | 65 | **Note:** Keep in mind, the correlation coefficient may not be statistically significant. It’s important not to rely on the regression line for predictions if the correlation is not significant. **Task:** *Step 6 of 6:* Calculate the coefficient of determination (\(R^2\)), and round your answer to three decimal places. **Answer:** Provide your answer in the input box provided. This example illustrates how regression analysis can help understand potential relationships between variables, such as time spent unsupervised and academic performance. However, remember to assess the significance of the correlation before making predictions.
The table below provides the number of hours spent unsupervised each day and the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, \(\hat{y} = b_0 + b_1x\), for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. | Hours Unsupervised | 0 | 1 | 1.5 | 3 | 4 | 4.5 | 5.5 | |--------------------|----|----|-----|----|----|-----|-----| | Overall Grades | 87 | 86 | 79 | 78 | 76 | 67 | 65 | **Step 5 of 6:** According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable \(\hat{y}\) is given by? - \( b_0 \) - \( b_1 \) - \( x \) - \( y \)
Transcribed Image Text:The table below provides the number of hours spent unsupervised each day and the overall grade averages for seven randomly selected middle school students. Using this data, consider the equation of the regression line, \(\hat{y} = b_0 + b_1x\), for predicting the overall grade average for a middle school student based on the number of hours spent unsupervised each day. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. | Hours Unsupervised | 0 | 1 | 1.5 | 3 | 4 | 4.5 | 5.5 | |--------------------|----|----|-----|----|----|-----|-----| | Overall Grades | 87 | 86 | 79 | 78 | 76 | 67 | 65 | **Step 5 of 6:** According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable \(\hat{y}\) is given by? - \( b_0 \) - \( b_1 \) - \( x \) - \( y \)
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