Question

You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is 0.793. How confident can you be that your predicted value will be reasonably close to the actual value? A. I can’t be confident at all; this is about as close to a random guess as you can get. B. I can be a little confident; it might be close, or it might be way off. C. I can be very confident; it will be close, but it probably won’t be exact. D. I can be certain that my predicted value will match the actual value exactly.

Answer 1

The correct option is c.

can be very confident; it will be close, but it probably won’t be exact.

Explanation:

Correlation coefficient r lies between -1 and +1 , if r is close to +1 the variables compared are highly positively correlated. If r is close to -1 then the variables compared are highly negatively correlated. If r is close to zero then the correlation between the variables compared is low. If r=0 then the variables compared do not correlate at all.

The closer the correlation coefficient is to +1, the better the prediction.

Therefore since r=0.793 , the correlation coefficient is close to +1 , it means there is a highly positive correlation between variables. Therefore the correct option is c. If r is exactly +1 then we can say without any shadow of doubt that the prediction will be perfect.