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?

ANSWER

Week 5 Discussion

Using the chart above, a strong and positive linear relationship between the sales and advertisements variables is observed. This is because as the values of advertisement costs increase, so do the values of sales increase (Illukkumbura, 2020).

From the regression equation, obtained from the data analysis-regression, a slope of 4.9216 is created. The slope establishes that, with a $1000 increase in advert costs, the sales would increase by $49,216. Hence, the H₀ would be that the slop is insignificant while the H₁ would be the slope is significant. The t=4.594315528 with a p-value ˂ 5% significance level show the rejection of the null hypothesis; thus, the slope is significant. H₁ ≠0.

The intercept is = -25.168, a value that is meaningless as sales cannot be negative. Regression coefficient, multiple r=0.823733296 with a coefficient determination of r^2 = 67.85%. This 67.85% tells us that there is a 67.8% sales variation, which is moderate and fit for the data. When X=950, yhat = -25.168+4.9216*950 = 4650.3518 and a regression of -20.2494. When the company/business spends $950,000 in an advertisement, the predicted sales are $4,650,351.8. We can conclude that this model underestimates the sales as when the advert costs used are $938,000; the sales are at $5,506,000.

Reference

Illukkumbura, A. (2020). Introduction to Regression Analysis. New York: Amazon Digital Services LLC.