Math Problem Statement

A small business is trying to determine the effect of a social media marketing campaign on sales. The plot below shows the relationship between the social media advertising costs and sales revenue. The linear regression output is shown below. R= What is the correlation between advertising costs and sales revenue?

A small business is trying to determine the effect of a social media marketing campaign on sales. The plot below shows the relationship between the social media advertising costs and sales revenue. The linear regression output is shown below. What is the correlation between advertising costs and sales revenue?

Solution

The correlation between social media advertising costs and sales revenue is given by the "Multiple R" value in the regression output table. In this case, the Multiple R value is 0.627615.

This indicates a moderate positive correlation between advertising costs and sales revenue. A value closer to 1 would represent a stronger positive correlation, while a value near 0 would suggest little to no correlation.

Would you like more details or have any questions about this analysis?

Here are 5 related questions that might interest you:

  1. How do we interpret the R-squared value in this context?
  2. What is the difference between R and R-squared in regression?
  3. How can the standard error help us understand the accuracy of this model?
  4. Why is the adjusted R-squared value lower than the R-squared value?
  5. What does the scatter plot suggest about the relationship between advertising costs and sales?

Tip: A higher correlation does not necessarily imply causation; it only suggests a relationship between the variables. Always explore other factors.

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Math Problem Analysis

Mathematical Concepts

Linear Regression
Correlation
Statistics

Formulas

Correlation coefficient (R)
R-squared value
Adjusted R-squared value

Theorems

Correlation Theorem
Linear Regression Assumptions

Suitable Grade Level

Undergraduate/Graduate Level