A random sample of 19 companies from the Forbes 500 list 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: profits = $\alpha$ + $\beta$ (sales), where the deviations were assumed to be independent and Normally distributed, with mean 0 and standard deviation $\sigma$. 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 Is there evidence 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 large. C)Yes, because the P-value for testing if the slope is 0 is quite small. D)It is impossible to say, because we are not given the actual value of the correlation.

Question

Quizplus · Accepted Answer

The P-value for testing if the slope is 0 is quite small, indicating that there is evidence of a significant linear relationship between sales and profits. Additionally, the positive correlation coefficient (r) also suggests a positive linear relationship between sales and profits.

A Random Sample of 19 Companies from the Forbes 500 α\alphaα

A Random Sample of 19 Companies from the Forbes 500 $\alpha$