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How to interpret regression analyses of population on sales

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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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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.

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See attached file.

The Abalone Fancy Fish Company sells exotic fish to high end restaurants throughout the West Coast. The sales manager wants to determine what, if any, relationship exists between the pounds/week of fish sold by 24 sales persons and the length of time (in years) the sales person has been with the company.

Attached is the Minitab regression output. The dependent variable is Sales (in pounds/week) and the independent variable is Experience (in years).

Use the Minitab output attached to identify and interpret the confidence and prediction intervals for 5 years experience.

For 5 years of experience, the 95% confidence interval: [ , ] *Round answer to three decimal places.

Interpretation of the 95% confidence interval:

A. This says we are 95% confident that any particular sales person with 5 years of experience will show sales between these values.
B. This says we are 95% confident that, in the population, sales persons making sales between these values will result in an additional 5 years with the company (on average).
C. This says we are 95% confident that across many sales persons with 5 years of experience, their mean sales will be between these values.
D. This says we are 95% confident that each additional year with the company will result in sales between these values.
E. This has no practical interpretation in this problem situation.

For 5 years of experience, the 95% prediction interval: [ , ] *Round answer to three decimal places.

Interpretation of the 95% prediction interval:
A. This says we are 95% confident that any particular sales person with 5 years of experience will show sales between these values.
B. This says we are 95% confident that, in the population, sales persons making sales between these values will result in an additional 5 years with the company (on average).
C. This says we are 95% confident that across many sales persons with 5 years of experience, their mean sales will be between these values.
D. This says we are 95% confident that each additional year with the company will result in sales between these values.
E. This has no practical interpretation in this problem situation.

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