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 |
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