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An advertising firm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The following bivariate data on twelve recent campaigns, including the cost of each campaign (denoted by x, in millions of dollars) and the resulting percentage increase in sales (denoted by y) following the campaign, were presented by the firm. A scatter plot of the data is shown in Figure 1. Campaign cost, x (in millions of dollars) Increase in sales, y (percent) 2.26 6.55 1.49 6.17 3.01 6.94 2.08 6.72 2.03 6.49 3.23 6.50 4.04 6.98 1.29 6.33 2.82 6.50 3.54 6.80 Campaign cost (in millions of dollars) 3.67 6.85 Figure 1 1.56 6.56 Send data to calculator Send data to Excel The value of the sample correlation coefficient r for these data is approximately 0.776. Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.) (a) What is the value of the slope of the least-squares regression line for these data? Round your answer to at least two decimal places. Increase in sales (percent)

An advertising firm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The following bivariate data on twelve recent campaigns, including the cost of each campaign (denoted by x, in millions of dollars) and the resulting percentage increase in sales (denoted by y) following the campaign, were presented by the firm. A scatter plot of the data is shown in Figure 1. Campaign cost, x (in millions of dollars) Increase in sales, y (percent) 2.26 6.55 1.49 6.17 3.01 6.94 2.08 6.72 2.03 6.49 3.23 6.50 4.04 6.98 1.29 6.33 2.82 6.50 3.54 6.80 Campaign cost (in millions of dollars) 3.67 6.85 Figure 1 1.56 6.56 Send data to calculator Send data to Excel The value of the sample correlation coefficient r for these data is approximately 0.776. Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below. (If necessary, consult a list of formulas.) (a) What is the value of the slope of the least-squares regression line for these data? Round your answer to at least two decimal places. Increase in sales (percent)

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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The image displays a statistical problem related to simple linear regression. It includes a table with data points, a description of a graph, and questions about the regression analysis. ### Data Table The data table provides the following points for analysis: | Campaign Cost (in millions of dollars) | Votes (in millions) | |----------------------------------------|---------------------| | 1.29 | 6.33 | | 2.82 | 6.50 | | 3.54 | 6.80 | | 3.67 | 6.85 | | 1.56 | 6.56 | ### Graph The graph is labeled as Figure 1 and illustrates a scatter plot for the data points described, with "Campaign cost (in millions of dollars)" on the x-axis and "Votes (in millions)" on the y-axis. ### Sample Correlation Coefficient The given sample correlation coefficient (r) for the data is approximately 0.776, indicating a moderate positive linear relationship between campaign cost and votes. ### Questions The following questions are posed for the users: (a) **What is the value of the slope of the least-squares regression line for these data?** Round your answer to at least two decimal places. (b) **What is the value of the y-intercept of the least-squares regression line for these data?** Round your answer to at least two decimal places. Users are instructed to carry intermediate computations to at least four decimal places, and they can use tools to send data to a calculator or Excel for further analysis.
Transcribed Image Text:The image displays a statistical problem related to simple linear regression. It includes a table with data points, a description of a graph, and questions about the regression analysis. ### Data Table The data table provides the following points for analysis: | Campaign Cost (in millions of dollars) | Votes (in millions) | |----------------------------------------|---------------------| | 1.29 | 6.33 | | 2.82 | 6.50 | | 3.54 | 6.80 | | 3.67 | 6.85 | | 1.56 | 6.56 | ### Graph The graph is labeled as Figure 1 and illustrates a scatter plot for the data points described, with "Campaign cost (in millions of dollars)" on the x-axis and "Votes (in millions)" on the y-axis. ### Sample Correlation Coefficient The given sample correlation coefficient (r) for the data is approximately 0.776, indicating a moderate positive linear relationship between campaign cost and votes. ### Questions The following questions are posed for the users: (a) **What is the value of the slope of the least-squares regression line for these data?** Round your answer to at least two decimal places. (b) **What is the value of the y-intercept of the least-squares regression line for these data?** Round your answer to at least two decimal places. Users are instructed to carry intermediate computations to at least four decimal places, and they can use tools to send data to a calculator or Excel for further analysis.
An advertising firm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The following bivariate data on twelve recent campaigns, including the cost of each campaign (denoted by \( x \), in millions of dollars) and the resulting percentage increase in sales (denoted by \( y \)) following the campaign, were presented by the firm. A scatter plot of the data is shown in Figure 1. **Table Data:** | Campaign cost, \( x \) (in millions of dollars) | Increase in sales, \( y \) (percent) | |------------------------------------------------|--------------------------------------| | 2.26 | 6.55 | | 1.49 | 6.17 | | 3.01 | 6.94 | | 2.08 | 6.72 | | 2.03 | 6.49 | | 3.23 | 6.58 | | 4.04 | 6.98 | | 1.29 | 6.33 | | 2.82 | 6.50 | | 3.54 | 6.80 | | 3.67 | 6.85 | | 1.56 | 6.56 | **Scatter Plot Description:** The scatter plot shows "Increase in sales (percent)" on the vertical axis and "Campaign cost (in millions of dollars)" on the horizontal axis. The data points suggest a positive relationship between campaign cost and increase in sales, with points moderately scattered around an upward trend. **Analysis:** - The value of the sample correlation coefficient \( r \) for these data is approximately 0.776, indicating a moderate positive correlation between campaign cost and increase in sales. **Question:** - (a) What is the value of the slope of the least-squares regression line for these data? Round your answer to at least two decimal places. **Actions:** - Buttons are available for sending data to a calculator or to Excel for further analysis.
Transcribed Image Text:An advertising firm wishes to demonstrate to its clients the effectiveness of the advertising campaigns it has conducted. The following bivariate data on twelve recent campaigns, including the cost of each campaign (denoted by \( x \), in millions of dollars) and the resulting percentage increase in sales (denoted by \( y \)) following the campaign, were presented by the firm. A scatter plot of the data is shown in Figure 1. **Table Data:** | Campaign cost, \( x \) (in millions of dollars) | Increase in sales, \( y \) (percent) | |------------------------------------------------|--------------------------------------| | 2.26 | 6.55 | | 1.49 | 6.17 | | 3.01 | 6.94 | | 2.08 | 6.72 | | 2.03 | 6.49 | | 3.23 | 6.58 | | 4.04 | 6.98 | | 1.29 | 6.33 | | 2.82 | 6.50 | | 3.54 | 6.80 | | 3.67 | 6.85 | | 1.56 | 6.56 | **Scatter Plot Description:** The scatter plot shows "Increase in sales (percent)" on the vertical axis and "Campaign cost (in millions of dollars)" on the horizontal axis. The data points suggest a positive relationship between campaign cost and increase in sales, with points moderately scattered around an upward trend. **Analysis:** - The value of the sample correlation coefficient \( r \) for these data is approximately 0.776, indicating a moderate positive correlation between campaign cost and increase in sales. **Question:** - (a) What is the value of the slope of the least-squares regression line for these data? Round your answer to at least two decimal places. **Actions:** - Buttons are available for sending data to a calculator or to Excel for further analysis.
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