# How to interpret regression analyses of population on sales

A bank has offices in six different markets. It is feasible to say the annual sales of offices are related to the population of the communities they are in. The dependent variable, y, is annual sales. The independent variable, x is market population.

A regression analysis was conducted using Excel and the results of this analysis are provided.

1) Based on this output, what can you conclude?

2) Interpret all results, write the regression equation, and state whether this analysis was fit or not in predicting sales from market population?

3) What does that mean for business?

Answer each question briefly

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#### Solution Preview

Your adjusted R^2 is .83 which suggests the equation fits the data points reasonably well. Your F-stat of 25.81 also suggests a good fit. In eyeballing the scatterplot it almost appears as though a 3rd degree polynomial would fit the data best. So, you may want to tinker with that idea in excel. Just add the trend line and choose 3rd degree polynomial and check the box for display equation and R^2.

Now for the specific questions

(1) Based on this output, what can you conclude? You could certainly conclude that there is a ...

#### Solution Summary

Given a regression of sales and population data I provide an analysis of the output. I discuss the R^2 value and the overall goodness of fit for the model. I discuss various possible functional forms for the equation given a scatter plot of the variables. Given the regression results I interpret the coefficients and their significance (t-stats) and how they relate to the theory that as population increases so too do sales. I discuss the implications for the bank operating in the markets studied.