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O d. r2 0.86 T x (Round to two decimal places) e. Interpret 2 There is a large variation in the amount of money that customers spend at the store, but if you only look at customers who spend a fixed amount of time at the store, this variation on average is reduced by 87% O Given any group that spends a fixed amount of time at the store, 87% of all of those customers will spend the predicted amount of money at the store. O There is a 87 % chance that the regression line will be a good predictor for the amount of money spent at the store based on the time spent at the store. O87% of all customers will spend the average amount of money at the store. ✓ OF f. The equation of the linear regression line is: ý (Please show your answers to two decimal places) g. Use the model to predict the amount of money spent by a customer who spends 16 minutes at the store. Dollars spent = (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: As x goes up, y goes up. noning since you cannot predict what any individual customer will

O d. r2 0.86 T x (Round to two decimal places) e. Interpret 2 There is a large variation in the amount of money that customers spend at the store, but if you only look at customers who spend a fixed amount of time at the store, this variation on average is reduced by 87% O Given any group that spends a fixed amount of time at the store, 87% of all of those customers will spend the predicted amount of money at the store. O There is a 87 % chance that the regression line will be a good predictor for the amount of money spent at the store based on the time spent at the store. O87% of all customers will spend the average amount of money at the store. ✓ OF f. The equation of the linear regression line is: ý (Please show your answers to two decimal places) g. Use the model to predict the amount of money spent by a customer who spends 16 minutes at the store. Dollars spent = (Please round your answer to the nearest whole number.) h. Interpret the slope of the regression line in the context of the question: As x goes up, y goes up. noning since you cannot predict what any individual customer will

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 d,f,and g
--- **Educational Resource on Linear Regression Analysis** **Understanding the Coefficient of Determination (r²)** - **d. \( r² \) Value:** \( 0.86 \) (Rounded to two decimal places) - **e. Interpretation of \( r² \):** - There is a large variation in the amount of money that customers spend at the store, but if you only look at customers who spend a fixed amount of time at the store, this variation on average is reduced by 87%. - Given any group that spends a fixed amount of time at the store, 87% of all of those customers will spend the predicted amount of money at the store. - There is an 87% chance that the regression line will be a good predictor for the amount of money spent at the store based on the time spent at the store. - 87% of all customers will spend the average amount of money at the store. **Note:** The correct interpretation is typically considered to be the first option in practical scenarios. **Formulation of the Linear Regression Equation** - **f. Equation of the Linear Regression Line:** \( \hat{y} = \_ + \_ x \) (Please show your answers to two decimal places) **Using the Linear Model for Predictions** - **g. Estimating Money Spent Based on Time:** Use the model to predict the amount of money spent by a customer who spends 16 minutes at the store. - **Dollars spent:** \( \_ \) (Please round your answer to the nearest whole number.) **Interpreting the Slope of the Regression Line** - **h. Interpretation of the Slope in Context:** - As \( x \) goes up, \( y \) goes up. - The slope is meaningless since you cannot predict what any individual customer will spend. --- This educational resource explains how to analyze and interpret linear regression results, specifically focusing on the coefficient of determination (\( r² \)), the formulation of the regression equation, using the model for predictions, and understanding the slope in the context of the given question. ---
Transcribed Image Text:--- **Educational Resource on Linear Regression Analysis** **Understanding the Coefficient of Determination (r²)** - **d. \( r² \) Value:** \( 0.86 \) (Rounded to two decimal places) - **e. Interpretation of \( r² \):** - There is a large variation in the amount of money that customers spend at the store, but if you only look at customers who spend a fixed amount of time at the store, this variation on average is reduced by 87%. - Given any group that spends a fixed amount of time at the store, 87% of all of those customers will spend the predicted amount of money at the store. - There is an 87% chance that the regression line will be a good predictor for the amount of money spent at the store based on the time spent at the store. - 87% of all customers will spend the average amount of money at the store. **Note:** The correct interpretation is typically considered to be the first option in practical scenarios. **Formulation of the Linear Regression Equation** - **f. Equation of the Linear Regression Line:** \( \hat{y} = \_ + \_ x \) (Please show your answers to two decimal places) **Using the Linear Model for Predictions** - **g. Estimating Money Spent Based on Time:** Use the model to predict the amount of money spent by a customer who spends 16 minutes at the store. - **Dollars spent:** \( \_ \) (Please round your answer to the nearest whole number.) **Interpreting the Slope of the Regression Line** - **h. Interpretation of the Slope in Context:** - As \( x \) goes up, \( y \) goes up. - The slope is meaningless since you cannot predict what any individual customer will spend. --- This educational resource explains how to analyze and interpret linear regression results, specifically focusing on the coefficient of determination (\( r² \)), the formulation of the regression equation, using the model for predictions, and understanding the slope in the context of the given question. ---
### Study on Relationship Between Time Spent in Store and Money Spent A grocery store manager conducted a survey to explore the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The results of the survey are displayed in the table below. #### Data from the Survey | Time (minutes) | 30 | 25 | 28 | 18 | 14 | 21 | 8 | |----------------|----|----|----|----|----|----|----| | Money (dollars) | 99 | 23 | 94 | 77 | 70 | 97 | 29 | #### Analysis 1. **Correlation Coefficient Calculation** - The correlation coefficient (r) is calculated to measure the strength and direction of the relationship between the two variables. - **Calculated r value**: 0.93 (rounded to 2 decimal places) 2. **Hypothesis Testing for Correlation** - **Null Hypothesis (H₀)**: \( \rho = 0 \) (There is no correlation between time spent in the store and money spent.) - **Alternative Hypothesis (H₁)**: \( \rho \neq 0 \) (There is a correlation between time spent in the store and money spent.) - **P-value**: 0.0020 (rounded to four decimal places) 3. **Conclusion Based on Significance Level** - Using a significance level (α) of 0.05: - **Decision Rule**: Reject the null hypothesis if p-value < α. - **Conclusion**: Since 0.0020 < 0.05, we reject the null hypothesis. - **Interpretation**: There is statistically significant evidence to conclude that there is a correlation between the amount of time a customer spends in the store and the amount of money they spend. #### Summary of Findings - The study finds a strong positive correlation (r = 0.93) between the time customers spend in the store and the amount of money they spend. - The hypothesis test confirms the presence of a significant correlation, as the p-value (0.0020) is less than the chosen significance level (0.05). This information can help store managers structure store layouts and marketing strategies to potentially increase the time customers spend in the store, thereby potentially increasing their
Transcribed Image Text:### Study on Relationship Between Time Spent in Store and Money Spent A grocery store manager conducted a survey to explore the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The results of the survey are displayed in the table below. #### Data from the Survey | Time (minutes) | 30 | 25 | 28 | 18 | 14 | 21 | 8 | |----------------|----|----|----|----|----|----|----| | Money (dollars) | 99 | 23 | 94 | 77 | 70 | 97 | 29 | #### Analysis 1. **Correlation Coefficient Calculation** - The correlation coefficient (r) is calculated to measure the strength and direction of the relationship between the two variables. - **Calculated r value**: 0.93 (rounded to 2 decimal places) 2. **Hypothesis Testing for Correlation** - **Null Hypothesis (H₀)**: \( \rho = 0 \) (There is no correlation between time spent in the store and money spent.) - **Alternative Hypothesis (H₁)**: \( \rho \neq 0 \) (There is a correlation between time spent in the store and money spent.) - **P-value**: 0.0020 (rounded to four decimal places) 3. **Conclusion Based on Significance Level** - Using a significance level (α) of 0.05: - **Decision Rule**: Reject the null hypothesis if p-value < α. - **Conclusion**: Since 0.0020 < 0.05, we reject the null hypothesis. - **Interpretation**: There is statistically significant evidence to conclude that there is a correlation between the amount of time a customer spends in the store and the amount of money they spend. #### Summary of Findings - The study finds a strong positive correlation (r = 0.93) between the time customers spend in the store and the amount of money they spend. - The hypothesis test confirms the presence of a significant correlation, as the p-value (0.0020) is less than the chosen significance level (0.05). This information can help store managers structure store layouts and marketing strategies to potentially increase the time customers spend in the store, thereby potentially increasing their
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