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 results were obtained from statistical software. Is there strong evidence of a straight-line relationship between sales and profits? Explain briefly.
A)Yes,because the slope of the least-squares line is positive
B)Yes,because the P-value for testing if the slope is zero 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.

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 results were obtained from statistical software.   Is there strong evidence of a straight-line relationship between sales and profits? Explain briefly.
A)Yes,because the slope of the least-squares line is positive 
B)Yes,because the P-value for testing if the slope is zero 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.

Quizplus · Accepted Answer

The P-value for testing if the slope is zero is less than 0.05, indicating strong evidence of a linear relationship between sales and profits. The slope being positive alone does not necessarily indicate a strong relationship, and the value of the correlation coefficient is not enough information to determine the strength of the relationship. We do not need the actual value of the correlation to make this conclusion.

A Random Sample of 79 Companies from the Forbes 500