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An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper's family and the grocery bill for that week. The graph below contains a scatterplot with a least-squares line. 200 180 160 140 120 100 80 60 40 20 0 0 200 400 600 800 1000 1200 Weekly Income One family reported a weekly income of $805. Estimate the residual (error) in their predicted grocery bill. Weekly Grocery Bil

An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained, and a questionnaire was administered asking about the weekly income of the shopper's family and the grocery bill for that week. The graph below contains a scatterplot with a least-squares line. 200 180 160 140 120 100 80 60 40 20 0 0 200 400 600 800 1000 1200 Weekly Income One family reported a weekly income of $805. Estimate the residual (error) in their predicted grocery bill. Weekly Grocery Bil

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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### Study on Association Between Weekly Income and Grocery Expenditures An economist conducted a study to explore the potential association between weekly income and weekly grocery expenditures. The primary interest was to determine whether higher income would lead to increased spending on groceries. #### Methodology - A random sample of shoppers at a local supermarket was obtained. - Participants were administered a questionnaire that inquired about their family's weekly income and the grocery bill for that week. #### Results The findings were visualized in a scatterplot, accompanied by a least-squares regression line. ![Scatterplot](#) The graph is described as follows: - **X-Axis (Horizontal):** Weekly Income (in dollars) - **Y-Axis (Vertical):** Weekly Grocery Bill (in dollars) - **Data Points (Blue Dots):** Each dot represents an individual family's reported weekly income and corresponding grocery bill. - **Least-Squares Line (Red Line):** A line that best fits the data points, showing the trend of how the grocery bill changes with income. #### Interpretation The scatterplot reveals a positive association between weekly income and weekly grocery expenditures, suggesting that, generally, as family income increases, so does the grocery bill. #### Example There is a specific case mentioned in the text: - One family reported a weekly income of $805. ##### Estimating the Residual (Error) - To estimate the residual, locate the point on the x-axis corresponding to $805. - Find where this point intersects the least-squares regression line, which provides the predicted grocery bill. - Compare this predicted value with the actual reported grocery bill of the family. The difference between these two values is the residual (error). This study provides valuable insights into consumer behavior, particularly the relationship between income levels and spending on groceries, which can inform economic policies and business strategies.
Transcribed Image Text:### Study on Association Between Weekly Income and Grocery Expenditures An economist conducted a study to explore the potential association between weekly income and weekly grocery expenditures. The primary interest was to determine whether higher income would lead to increased spending on groceries. #### Methodology - A random sample of shoppers at a local supermarket was obtained. - Participants were administered a questionnaire that inquired about their family's weekly income and the grocery bill for that week. #### Results The findings were visualized in a scatterplot, accompanied by a least-squares regression line. ![Scatterplot](#) The graph is described as follows: - **X-Axis (Horizontal):** Weekly Income (in dollars) - **Y-Axis (Vertical):** Weekly Grocery Bill (in dollars) - **Data Points (Blue Dots):** Each dot represents an individual family's reported weekly income and corresponding grocery bill. - **Least-Squares Line (Red Line):** A line that best fits the data points, showing the trend of how the grocery bill changes with income. #### Interpretation The scatterplot reveals a positive association between weekly income and weekly grocery expenditures, suggesting that, generally, as family income increases, so does the grocery bill. #### Example There is a specific case mentioned in the text: - One family reported a weekly income of $805. ##### Estimating the Residual (Error) - To estimate the residual, locate the point on the x-axis corresponding to $805. - Find where this point intersects the least-squares regression line, which provides the predicted grocery bill. - Compare this predicted value with the actual reported grocery bill of the family. The difference between these two values is the residual (error). This study provides valuable insights into consumer behavior, particularly the relationship between income levels and spending on groceries, which can inform economic policies and business strategies.
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