You are the vice president of sales for TerraFirma, a company that manufactures

Question

You are the vice president of sales for TerraFirma, a company that manufactures outdoor sporting gear. You receive a report on your desk one morning that claims little or no relationship between the University of Michigan Consumer Sentiment Index (CSI) and outdoor sporting gear sales. The claim is based on a very low R2 of the simple regression model, using these two variables (CSI and sales). Discuss how you would (or should) react to this report and why. What clarifying questions might you ask? Please answer with an original post, not one already used. Discuss how you would react to the report and what clarifying questions would you ask?

Explanation / Answer

The questions we can ask in this situation might include,

We can obtain a sample size, including more data related to University of Michigan Consumer Sentiment Index (CSI) and outdoor sporting gear sales.

When the data is received, we can check if the data is too small, there might be a relation between the two variables and in that case, a hypothesis test to check the dependency of the variables has to be conducted.

Andon the other hand, if the data is large, is no relationship between the two Variables University of Michigan Consumer Sentiment Index (CSI) and outdoor sporting gear sales. Since R-squared is very low, we can say that low percentage or zero percentage of variance of sales is explained by CSI variable.
I believe that In order to understand the meaning of the R2 result, we should know its characteristics that are why I will list bellow some of the R2 characteristics:
a) The result of R2 is usually between 0 and 1 and with no units
b) The higher the result the more the data is fitting
C) When the result of R2 is 0 => knowing X does not help you to anticipate the value of Y
D) When the result of R2 is 0 => there is no meaningful relationship between X and Y
E) When the result of R2 is 0 => knowing X does help you to anticipate the value of Y
F) When the result of R2 is 0 => there is a meaningful relationship between X and Y

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