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 (in millions of dollars) and the resulting percentage increase in sales following the campaign, were presented by the firm. Based on these data, we would compute the least-squares regression line to be y = 6.20 + 0.17x, with x representing campaign cost and y representing the resulting percentage increase in sales. (This line is shown below, along with a scatter plot of the data.) Campalgn Increase in cost, x sales, y (percent) (in millions of dollars) 2.34 7.2- 6.70 1.25 6.34 1.99 6.51 6. 1.70 6.28 6.6- 3.70 6.74 1.57 6.56 2.12 6.74 6.2 3.24 6.53 2.89 6.58 3.01 6.91 3.44 6.86 Campaign cost, x (in millions of dollars) 4.12 6.92 Send data to calculator v Send data to Excel Based on the sample data and the regression line, complete the following. (a) For these data, values for campaign cost that are greater than the mean of the values for campaign cost tend to be paired with values for percentage increase in sales that are (Choose one) | the mean of the values for percentage increase in ? sales. (b) According to the regression equation, for an increase of one milion dollars in advertising campaign cost, there is a corresponding (Choose one) ▼ of 0.17 percent in sales. (c) What was the observed percentage increase in sales when the advertising campaign cost was 2.12 million dollars? |(d) From the regression equation, what is the predicted percentage increase in sales when the advertising campaign cost is 2.12 million dollars? (Round your answer to at least two decimal places.) Increase in sales, y
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 (in millions of dollars) and the resulting percentage increase in sales following the campaign, were presented by the firm. Based on these data, we would compute the least-squares regression line to be y = 6.20 + 0.17x, with x representing campaign cost and y representing the resulting percentage increase in sales. (This line is shown below, along with a scatter plot of the data.) Campalgn Increase in cost, x sales, y (percent) (in millions of dollars) 2.34 7.2- 6.70 1.25 6.34 1.99 6.51 6. 1.70 6.28 6.6- 3.70 6.74 1.57 6.56 2.12 6.74 6.2 3.24 6.53 2.89 6.58 3.01 6.91 3.44 6.86 Campaign cost, x (in millions of dollars) 4.12 6.92 Send data to calculator v Send data to Excel Based on the sample data and the regression line, complete the following. (a) For these data, values for campaign cost that are greater than the mean of the values for campaign cost tend to be paired with values for percentage increase in sales that are (Choose one) | the mean of the values for percentage increase in ? sales. (b) According to the regression equation, for an increase of one milion dollars in advertising campaign cost, there is a corresponding (Choose one) ▼ of 0.17 percent in sales. (c) What was the observed percentage increase in sales when the advertising campaign cost was 2.12 million dollars? |(d) From the regression equation, what is the predicted percentage increase in sales when the advertising campaign cost is 2.12 million dollars? (Round your answer to at least two decimal places.) Increase in sales, y
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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![### Educational Website Content: Evaluating Advertising Campaign Effectiveness
**Overview:**
An advertising firm evaluates the effectiveness of its campaigns by presenting bivariate data concerning twelve different marketing efforts. The data consists of campaign costs (in millions of dollars) and the resulting percentage increase in sales.
**Data Table:**
| Campaign Cost (in millions of dollars) | Increase in Sales (%) |
|---------------------------------------|-----------------------|
| 2.34 | 6.70 |
| 1.25 | 6.34 |
| 1.99 | 6.51 |
| 1.70 | 6.28 |
| 3.70 | 6.74 |
| 1.57 | 6.56 |
| 2.12 | 6.74 |
| 3.24 | 6.53 |
| 2.89 | 6.58 |
| 3.01 | 6.91 |
| 3.44 | 6.86 |
| 4.12 | 6.92 |
**Statistical Analysis:**
The least-squares regression line calculated for this data is:
\[ y = 6.20 + 0.17x \]
where \( y \) represents the percentage increase in sales and \( x \) represents the campaign cost.
**Graphical Representation:**
A scatter plot is presented with campaign cost on the x-axis and percentage increase in sales on the y-axis. Each point represents a campaign's cost and corresponding increase in sales, with a regression line illustrating the relationship.
### Questions and Interpretation:
1. **Mean Comparison:**
- Analyze how campaign costs above the mean associate with sales increases relative to their mean.
2. **Regression Equation Insight:**
- Determine the sales increase associated with a $1 million rise in campaign cost.
3. **Observed Data:**
- Identify the percentage increase in sales for a specific campaign cost of $2.12 million.
4. **Predicted Values:**
- Calculate the predicted sales percentage increase for a campaign cost of $2.12 million using the regression equation.
This educational exercise provides a practical application of statistics in marketing, enhancing understanding of data analysis and prediction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe53f16ab-a658-43ea-87b0-0607d7296018%2F89df58f4-a03a-4d10-a59c-bd8253db4577%2Fwbd2gxo_processed.png&w=3840&q=75)
Transcribed Image Text:### Educational Website Content: Evaluating Advertising Campaign Effectiveness
**Overview:**
An advertising firm evaluates the effectiveness of its campaigns by presenting bivariate data concerning twelve different marketing efforts. The data consists of campaign costs (in millions of dollars) and the resulting percentage increase in sales.
**Data Table:**
| Campaign Cost (in millions of dollars) | Increase in Sales (%) |
|---------------------------------------|-----------------------|
| 2.34 | 6.70 |
| 1.25 | 6.34 |
| 1.99 | 6.51 |
| 1.70 | 6.28 |
| 3.70 | 6.74 |
| 1.57 | 6.56 |
| 2.12 | 6.74 |
| 3.24 | 6.53 |
| 2.89 | 6.58 |
| 3.01 | 6.91 |
| 3.44 | 6.86 |
| 4.12 | 6.92 |
**Statistical Analysis:**
The least-squares regression line calculated for this data is:
\[ y = 6.20 + 0.17x \]
where \( y \) represents the percentage increase in sales and \( x \) represents the campaign cost.
**Graphical Representation:**
A scatter plot is presented with campaign cost on the x-axis and percentage increase in sales on the y-axis. Each point represents a campaign's cost and corresponding increase in sales, with a regression line illustrating the relationship.
### Questions and Interpretation:
1. **Mean Comparison:**
- Analyze how campaign costs above the mean associate with sales increases relative to their mean.
2. **Regression Equation Insight:**
- Determine the sales increase associated with a $1 million rise in campaign cost.
3. **Observed Data:**
- Identify the percentage increase in sales for a specific campaign cost of $2.12 million.
4. **Predicted Values:**
- Calculate the predicted sales percentage increase for a campaign cost of $2.12 million using the regression equation.
This educational exercise provides a practical application of statistics in marketing, enhancing understanding of data analysis and prediction.
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