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d. What is the strength and direction of the correlation? Explain how you know. How much variability in the model for happiness is due to the number of hours of sleep? f. According to the results of the test, would you say that the amount that a person sleeps is related to their happiness? Explain, using the data and results from the test. Answers without explanation using the statistics collected will not be given credit.

d. What is the strength and direction of the correlation? Explain how you know. How much variability in the model for happiness is due to the number of hours of sleep? f. According to the results of the test, would you say that the amount that a person sleeps is related to their happiness? Explain, using the data and results from the test. Answers without explanation using the statistics collected will not be given credit.

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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**Transcription for Educational Website:** --- ### Analyzing the Relationship Between Sleep and Happiness #### Questions: a. **Which is the explanatory and which is the response variable?** b. **According to the scatterplot above, what were the happiness scores for the three people who slept 5.5 hours?** c. **According to the scatterplot, does there appear to be a linear relationship between the variables? Explain how you know.** d. **What is the strength and direction of the correlation? Explain how you know.** e. **How much variability in the model for happiness is due to the number of hours of sleep?** f. **According to the results of the test, would you say that the amount that a person sleeps is related to their happiness? Explain, using the data and results from the test. Answers without explanation using the statistics collected will not be given credit.** g. **Use the regression formula above to predict the following. Show your work to three decimal places:** - i. Number of hours of sleep=8.0, Happiness score=? - ii. Number of hours of sleep=5.5, Happiness score=? - iii. Happiness score=7, Number of hours of sleep=? --- **Explanation of Graphs or Diagrams:** *(Since the image with scatterplot and regression formula is not visible, a generic explanation is provided)* - **Scatterplot:** A graphical representation showing the relationship between the number of hours of sleep (explanatory variable) and happiness scores (response variable). Each point on the scatterplot represents an individual’s data for these two variables. - **Regression Line:** If present, the regression line indicates the best fit through the points on the scatterplot, showing the general trend of how the happiness score changes with the number of hours of sleep. - **Correlation Coefficient:** This might be indicated in the graph or explanation, showing the strength and direction of the linear relationship between sleep and happiness. Correlation coefficients range from -1 to 1. Understanding this relationship helps to analyze how an increase in sleep might affect happiness scores, and vice versa. Answering the provided questions using statistical methods such as correlation analysis and regression helps in academic and practical applications related to health and well-being.
Transcribed Image Text:**Transcription for Educational Website:** --- ### Analyzing the Relationship Between Sleep and Happiness #### Questions: a. **Which is the explanatory and which is the response variable?** b. **According to the scatterplot above, what were the happiness scores for the three people who slept 5.5 hours?** c. **According to the scatterplot, does there appear to be a linear relationship between the variables? Explain how you know.** d. **What is the strength and direction of the correlation? Explain how you know.** e. **How much variability in the model for happiness is due to the number of hours of sleep?** f. **According to the results of the test, would you say that the amount that a person sleeps is related to their happiness? Explain, using the data and results from the test. Answers without explanation using the statistics collected will not be given credit.** g. **Use the regression formula above to predict the following. Show your work to three decimal places:** - i. Number of hours of sleep=8.0, Happiness score=? - ii. Number of hours of sleep=5.5, Happiness score=? - iii. Happiness score=7, Number of hours of sleep=? --- **Explanation of Graphs or Diagrams:** *(Since the image with scatterplot and regression formula is not visible, a generic explanation is provided)* - **Scatterplot:** A graphical representation showing the relationship between the number of hours of sleep (explanatory variable) and happiness scores (response variable). Each point on the scatterplot represents an individual’s data for these two variables. - **Regression Line:** If present, the regression line indicates the best fit through the points on the scatterplot, showing the general trend of how the happiness score changes with the number of hours of sleep. - **Correlation Coefficient:** This might be indicated in the graph or explanation, showing the strength and direction of the linear relationship between sleep and happiness. Correlation coefficients range from -1 to 1. Understanding this relationship helps to analyze how an increase in sleep might affect happiness scores, and vice versa. Answering the provided questions using statistical methods such as correlation analysis and regression helps in academic and practical applications related to health and well-being.
### Impact of Sleep on Happiness - Educational Analysis #### Use the following information to answer questions a-g. **Study Overview:** You have a theory that increasing the amount of sleep that a person gets will make them happier. In order to test this, you collected a simple random sample of 18 people and tracked how much they sleep on average for three weeks. Subsequently, you asked them to rate how happy they were on a 10-point scale. The ratings range as follows: - 1 (Miserable) - 5 (Mediocre) - 10 (Joyful) The following are the results from this test. **Graph Explanation:** The scatter plot shows the relationship between the number of hours of sleep and the happiness score. The x-axis represents the hours of sleep ranging from 5 to 9 hours. The y-axis indicates the happiness score, from 3 (miserable) to 9 (joyful). **Data Summary:** - **Happiness Score Equation**: \( \text{Happiness Score} = -3.8601533 + 1.4482759 \times \text{Hours of Sleep} \) - **Sample Size**: 18 - **Correlation Coefficient (R)**: 0.93478344 - **R-squared (R-sq)**: 0.87382007 **Analysis:** The scatter plot indicates a positive correlation between the number of hours of sleep and the happiness score. As the number of hours of sleep increases, the happiness score also tends to increase. **Statistical Metrics Explained:** 1. **Happiness Score Equation**: This linear equation suggests that with each additional hour of sleep, the happiness score increases by approximately 1.4483 points. 2. **Sample Size**: The study includes data from 18 individuals. 3. **Correlation Coefficient (R)**: A value of 0.93478344 indicates a very strong positive correlation between sleep and happiness. 4. **R-squared (R-sq)**: This value of 0.87382007 means that approximately 87.38% of the variability in happiness scores can be explained by the variability in the number of hours slept. **Conclusion:** The study supports the theory that longer sleep duration tends to result in higher happiness scores among individuals. The strong correlation and high R-squared value underline the reliability of the findings. This data suggests that promoting
Transcribed Image Text:### Impact of Sleep on Happiness - Educational Analysis #### Use the following information to answer questions a-g. **Study Overview:** You have a theory that increasing the amount of sleep that a person gets will make them happier. In order to test this, you collected a simple random sample of 18 people and tracked how much they sleep on average for three weeks. Subsequently, you asked them to rate how happy they were on a 10-point scale. The ratings range as follows: - 1 (Miserable) - 5 (Mediocre) - 10 (Joyful) The following are the results from this test. **Graph Explanation:** The scatter plot shows the relationship between the number of hours of sleep and the happiness score. The x-axis represents the hours of sleep ranging from 5 to 9 hours. The y-axis indicates the happiness score, from 3 (miserable) to 9 (joyful). **Data Summary:** - **Happiness Score Equation**: \( \text{Happiness Score} = -3.8601533 + 1.4482759 \times \text{Hours of Sleep} \) - **Sample Size**: 18 - **Correlation Coefficient (R)**: 0.93478344 - **R-squared (R-sq)**: 0.87382007 **Analysis:** The scatter plot indicates a positive correlation between the number of hours of sleep and the happiness score. As the number of hours of sleep increases, the happiness score also tends to increase. **Statistical Metrics Explained:** 1. **Happiness Score Equation**: This linear equation suggests that with each additional hour of sleep, the happiness score increases by approximately 1.4483 points. 2. **Sample Size**: The study includes data from 18 individuals. 3. **Correlation Coefficient (R)**: A value of 0.93478344 indicates a very strong positive correlation between sleep and happiness. 4. **R-squared (R-sq)**: This value of 0.87382007 means that approximately 87.38% of the variability in happiness scores can be explained by the variability in the number of hours slept. **Conclusion:** The study supports the theory that longer sleep duration tends to result in higher happiness scores among individuals. The strong correlation and high R-squared value underline the reliability of the findings. This data suggests that promoting
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d)

According to the provided information, the correlation coefficient is 0.9348 (close to 1 and positive). Therefore, there is strong strength of association between the variables and direction is positive.

 

e)

According to the provide information, the coefficient of determination (R2) is 0.8738. Therefore, 87.38% variability in the model for happiness is due to the number of hour of sleep.

 

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