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 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 on the advertisement. Does the model underestimate or overestimate ales?