Patterns and Modeling

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 advertising expenditures and sales revenues.

Consider the following dataset:

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 and answer the following questions:

• 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 if the business spends \$950,000 on advertising. Does the model underestimate or overestimate sales?

Prepare your graphical and written response in no less than 500 words.

 Advertising (\$’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