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