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 underestimates or overestimates ales?
(1) Explain the difference between correlation and cause and effect. Give examples to explain each concept.

(2) Explain the difference between simple linear regression and multiple regression. Give examples to explain each concept.

(3) What does a scatter plot tell us? What does a scatter plot not able to tell us? How do you determine that a scatter plot might be helpful in visualizing the overall outcome?

(4) Why do you think that regression analysis is used more in the workplace more often than cause and effect?

Sample Solution