Consider the following sample data for the relationship between advertising budget and sales for Product A:

Observation

1

2

3

4

5

6

7

8

9

10

Advertising ($)

90,000

100,000

100,000

110,000

120,000

120,000

130,000

140,000

140,000

150,000

Sales ($)

535,000

626,000

625,000

674,000

712,000

725,000

809,000

832,000

845,000

919,000

**What is the predicted sales quantity for an advertising budget of $119,000?**

To predict the sales quantity for an advertising budget of $119,000, we can use a simple linear regression model. Linear regression estimates the relationship between the independent variable (advertising budget) and the dependent variable (sales).

### Steps:

1. **Identify the independent and dependent variables:**
   - Independent variable (X): Advertising budget.
   - Dependent variable (Y): Sales.

2. **Use the linear regression equation:**
   \[
   \hat{Y} = \beta_0 + \beta_1 X
   \]
   Where:
   - $ \hat{Y} $ is the predicted sales.
   - $ X $ is the advertising budget.
   - $ \beta_0 $ is the y-intercept (constant).
   - $ \beta_1 $ is the slope (rate of change in sales for a unit increase in advertising budget).

I will calculate the regression coefficients and predict the sales for an advertising budget of $119,000. Let me calculate that for you.The predicted sales quantity for an advertising budget of $119,000 is approximately **$724,258**.

Would you like more details or have any questions?

Here are 5 related questions you might find helpful:
1. How is the slope ($ \beta_1 $) of a linear regression line calculated?
2. What other methods can be used to predict sales from an advertising budget?
3. How accurate is the linear regression model in this case?
4. What happens if the relationship between advertising and sales is nonlinear?
5. Can we use multiple regression if we have other factors besides advertising?

**Tip:** Always check the goodness of fit (e.g., $ R^2 $) when using linear regression to assess how well the model explains the data.

What is the predicted sales quantity for an advertising budget of $119,000?

Discover how to predict the sales quantity for Product A using linear regression with an advertising budget of $119,000. This example walks through the use of a linear regression model with a detailed step-by-step solution, ideal for students in Grades 11-12 or college-level statistics courses.

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