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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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I need help with f, g and h
--- **Study on the Relationship Between Phone Usage and Weight** **Research Question:** What is the relationship between the number of minutes per day a woman spends talking on the phone and the woman's weight? The time on the phone and weight for 8 women are shown in the table below. | Time (minutes) | 81 | 52 | 52 | 64 | 62 | 23 | 36 | 30 | |----------------|----|----|----|----|----|----|----|----| | Pounds | 119| 119| 116| 117| 128| 105| 116| 105| ### a. Correlation Coefficient - Find the correlation coefficient: \( r = \) ⬜ (Round to 2 decimal places.) ### b. Hypothesis for Correlation - The null and alternative hypotheses for correlation are: - \( H_0 \): ⬜ \( = 0 \) - \( H_1 \): ⬜ \( \neq 0 \) - The p-value is: \(\_\_\_\_\_\_\_\_\_\_\_\) (Round to four decimal places.) ### c. Hypothesis Test Conclusion - Use a level of significance of \(\alpha = 0.05\) to state the conclusion of the hypothesis test in the context of the study. - There is statistically significant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the regression line is useful. - There is statistically significant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone. - There is statistically insignificant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the use of the regression line is not appropriate. - There is statistically insignificant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone. ### d. Coefficient of Determination - \( r^2 = \) ⬜ (Round to two decimal places.) ### e. Interpretation of \( r^2 \) - There is a 56% chance that the regression line will be a good predictor for women's weight based on their time spent on the phone. - 56% of all women will have
Transcribed Image Text:--- **Study on the Relationship Between Phone Usage and Weight** **Research Question:** What is the relationship between the number of minutes per day a woman spends talking on the phone and the woman's weight? The time on the phone and weight for 8 women are shown in the table below. | Time (minutes) | 81 | 52 | 52 | 64 | 62 | 23 | 36 | 30 | |----------------|----|----|----|----|----|----|----|----| | Pounds | 119| 119| 116| 117| 128| 105| 116| 105| ### a. Correlation Coefficient - Find the correlation coefficient: \( r = \) ⬜ (Round to 2 decimal places.) ### b. Hypothesis for Correlation - The null and alternative hypotheses for correlation are: - \( H_0 \): ⬜ \( = 0 \) - \( H_1 \): ⬜ \( \neq 0 \) - The p-value is: \(\_\_\_\_\_\_\_\_\_\_\_\) (Round to four decimal places.) ### c. Hypothesis Test Conclusion - Use a level of significance of \(\alpha = 0.05\) to state the conclusion of the hypothesis test in the context of the study. - There is statistically significant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the regression line is useful. - There is statistically significant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone. - There is statistically insignificant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the use of the regression line is not appropriate. - There is statistically insignificant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone. ### d. Coefficient of Determination - \( r^2 = \) ⬜ (Round to two decimal places.) ### e. Interpretation of \( r^2 \) - There is a 56% chance that the regression line will be a good predictor for women's weight based on their time spent on the phone. - 56% of all women will have
### Linear Regression Analysis #### Reducing Variation in Predictions - There is a large variation in women's weight, but if you only look at women with a fixed weight, this variation on average is reduced by 56%. - Given any group of women who all weigh the same amount, 56% of all these women will weigh the predicted amount. #### Linear Regression Equation **f. The equation of the linear regression line is:** \[ \hat{y} = \_\_\_\_ + \_\_\_\_x \] *(Please show your answers to two decimal places)* #### Predicting Weight Based on Time Spent on the Phone **g. Use the model to predict the weight of a woman who spends 40 minutes on the phone.** \[ \text{Weight} = \_\_\_\_ \] *(Please round your answer to the nearest whole number.)* #### Interpreting the Slope in Context **h. Interpret the slope of the regression line in the context of the question:** - \[ \circ \] As x goes up, y goes up. - \[ \circ \] For every additional minute women spend on the phone, they tend to weigh on average 0.29 additional pounds. - \[ \circ \] The slope has no practical meaning since you cannot predict a woman's weight. #### Interpreting the Y-Intercept in Context **i. Interpret the y-intercept in the context of the question:** - \[ \circ \] The average woman's weight is predicted to be 101. - \[ \circ \] If a woman does not spend any time talking on the phone, then that woman will weigh 101 pounds. - \[ \circ \] The y-intercept has no practical meaning for this study. - \[ \circ \] The best prediction for the weight of a woman who does not spend any time talking on the phone is 101 pounds. ### Additional Resources - [Helpful Video on the Linear Regression Line](#) - [Helpful Video on Correlation](#) - [Helpful Video on Hypothesis Tests for Correlation](#) ### Hints [+] Click on the links above for detailed instructional videos and further reading materials on each topic.
Transcribed Image Text:### Linear Regression Analysis #### Reducing Variation in Predictions - There is a large variation in women's weight, but if you only look at women with a fixed weight, this variation on average is reduced by 56%. - Given any group of women who all weigh the same amount, 56% of all these women will weigh the predicted amount. #### Linear Regression Equation **f. The equation of the linear regression line is:** \[ \hat{y} = \_\_\_\_ + \_\_\_\_x \] *(Please show your answers to two decimal places)* #### Predicting Weight Based on Time Spent on the Phone **g. Use the model to predict the weight of a woman who spends 40 minutes on the phone.** \[ \text{Weight} = \_\_\_\_ \] *(Please round your answer to the nearest whole number.)* #### Interpreting the Slope in Context **h. Interpret the slope of the regression line in the context of the question:** - \[ \circ \] As x goes up, y goes up. - \[ \circ \] For every additional minute women spend on the phone, they tend to weigh on average 0.29 additional pounds. - \[ \circ \] The slope has no practical meaning since you cannot predict a woman's weight. #### Interpreting the Y-Intercept in Context **i. Interpret the y-intercept in the context of the question:** - \[ \circ \] The average woman's weight is predicted to be 101. - \[ \circ \] If a woman does not spend any time talking on the phone, then that woman will weigh 101 pounds. - \[ \circ \] The y-intercept has no practical meaning for this study. - \[ \circ \] The best prediction for the weight of a woman who does not spend any time talking on the phone is 101 pounds. ### Additional Resources - [Helpful Video on the Linear Regression Line](#) - [Helpful Video on Correlation](#) - [Helpful Video on Hypothesis Tests for Correlation](#) ### Hints [+] Click on the links above for detailed instructional videos and further reading materials on each topic.
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