Describing and summarizing relationships between variables.

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)
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 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?

Sample Solution