A random sample of 79 companies from the Forbes 500 list (which actually consist

Question

A random sample of 79 companies from the Forbes 500 list (which actually consists of nearly 800 companies) was selected, and the relationship between sales (in hundreds of thousands of dollars) and profits (in hundreds of thousands of dollars) was investigated by regression. The following simple linear regression model was used    Profitsi = 0 + 1(Sales)i + i where the deviations i were assumed to be independent and normally distributed, with mean 0 and standard deviation . This model was fit to the data using the method of least squares. The following results were obtained from statistical software. R2 = 0.662 s = 466.2

Variable Parameter est. Std. err. of parameter est. Constant –176.644 61.16 Sales 0.092498 0.0075

Is there strong evidence (and if so, why) of a straight line relationship between sales and profits? a. Yes, because the slope of the least-squares line is positive.

b. Yes, because the P-value for testing if the slope is 0 is quite small.

c. No, because the value of the square of the correlation is relatively small.

d. It is impossible to say, because we are not given the actual value of the correlation.

Explanation / Answer

As should be noted an R^2 of 0.662 is a decent value for a regression.

In most cases,even an R^2 of 0.4 is also considered good.

But the slope being positive or negative doesnt serve the case of strong evidence

Yes the P-value does effect,Smaller the P-value better it is.---------->Option B)

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