A researcher took a sample of 25 electronics companies and found the following r

Question

A researcher took a sample of 25 electronics companies and found the following relationship between x and y, where x is the amount of money (in millions of dollars) spent on advertising by a company in 2009 and y represents the total gross sales (in millions of dollars) of that company for 2009. y = 3.6 + 11.75 x An electronics company spent $2 million on advertising in 2009. What are its expected gross sales for 2009? b. Suppose four electronics companies spent$2 million each on advertising in 2009. Do you expect these four companies to have the same actual gross sales for 2009? Explain e. Is the relationship between x and y exact or not exact?

Explanation / Answer

The Linear model is

Y^ = 3.6 + 11.75 x^

(a) spent = 2 millions

so Total gross sales = 3.6 + 11.75* 2 = $27.1 million dollars

(b) No, if we calculate total gross sales from this model, this can give us a fair estimate of total gross sales from the amount spent on advertising for any company. This is a prediction estimate of Gross sales. Here we can draw a confidence interval around the predicted interval and there is very high chance that gross sales will fall in this interval. As given in the question, these 4 companies will have total gross sales nearly around 27.1 million dollars as estimated above but not the exactly same value.

(c) A collinear relationship is required for an exact relationship.Here Coefficient of determination must be equal to 1 to have an exact relationship. Here we don't know about R. So, we will check the given model. Here there are 25 companies on which regression has been performed so we can predict that this is not an exact relationship. Because, there are other factors, like product quality, plant and market location which put impact on this collinear relationship. So, this is just a trend line not an exact linear relationship.

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