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# Discussion – Patterns And Modeling

Respond to the following in a minimum of 175 words:

Models help us describe and summarize relationships between variables. Understanding how process variables relate helps businesses predict and improve performance. For example, a marketing manager might be interested in modeling the relationship between advertisement expenditures and sales revenues.

## Discussion – Patterns And Modeling

**Consider** the dataset below and respond to the questions that follow:

Advertisement ($’000) Sales ($’000)

1068 4489

1026 5611

767 3290

885 4113

1156 4883

1146 5425

892 4414

938 5506

769 3346

677 3673

1184 6542

1009 5088

- 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 in
*Fitting a Regression on a Scatter Plot*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 an advertisement. Does the model underestimate or overestimate sales?