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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:

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?