Correlation & Regression

A company is interested in studying the relationship between the number of ads placed and sales (in millions of dollars). The data below shows the results in 15 equivalent markets.

Compute each of the following using the formulas. When you are finished, check your work using MS Excel.

a) Find the correlation coefficient.

b) Compute the regression coefficients and state the regression equation.

c) Using the regression model,

• What is your predicted sales if no ads are placed?
• What is your predicted sales if you place 10 ads?

​

^{Xi (# ads) Yi (sales in millions}

5 7

6 9

4 8

5 8

6 7

3 6

7 10

4 7

7 14

9 15

8 11

6 9

10 20

2 4

1 2

This is the problem you got via email.

A company is interested in studying the relationship between the number of ads placed and sales (in millions of dollars). The data below shows the results in 15 equivalent markets.

a) Find the correlation coefficient.

A company is interested in studying the relationship between the number of ads placed and sales (in millions of dollars). The data below shows the results in 15 equivalent markets.

b) Compute the regression coefficients and state the regression equation.

A company is interested in studying the relationship between the number of ads placed and sales (in millions of dollars). The data below shows the results in 15 equivalent markets.

c) Using the regression model,

• What is your predicted sales if no ads are placed?
• What is your predicted sales if you place 10 ads?

A company is interested in studying the relationship between the number of ads placed and sales (in millions of dollars). The data below shows the results in 15 equivalent markets.

What are the meanings of the regression coefficients?

​

b₀ we have already seen. That is the Y-intercept, the value of Y (sales) when X (# ads) = 0)

​

Meaning of slope term (b₁) – for every additional ad you place, the sales increase by $1.663 million

A company is interested in studying the relationship between the number of ads placed and sales (in millions of dollars). The data shows the results in 15 equivalent markets.

From MS Excel:

A company is interested in studying the relationship between the number of ads placed and sales (in millions of dollars). The data shows the results in 15 equivalent markets.

From MS Excel: