Models help us describe and summarize relationships between variables. Understanding how process variables relate to each other helps businesses predict and improve performance. For example, a marketing manager might be interested in modeling the relationship between advertisement expenditures and sales revenues.
Consider the dataset below and respond to the questions that follow:
Advertisement ($’000) Sales ($’000)
- Construct a scatter plot with this data.
- Do you observe a relationship between both variables?
- Use Excel to fit a linear regression line to the data. What is the fitted regression model? (Hint: You can follow the steps outlined on page 497 of the textbook.)
- What is the slope? What does the slope tell us? Is the slope significant?
- What is the intercept? Is it meaningful?
- What is the value of the regression coefficient,r? What is the value of the coefficient of determination, r^2? What does r^2 tell us?
- Use the model to predict sales and the business spends $950,000 in advertisement. Does the model underestimate or overestimates ales?