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 1. How confident can you be that your predicted value will be reasonably close to the actual value?
I can’t be confident at all; this is about as close to a random guess as you can get.
I can be a little confident; it might be close, or it might be way off. There is a 50/50 chance.
I can be very confident; it will be close, but it probably won’t be exact.
I can be certain that my predicted value will match the actual value exactly.
The correct answer is: I can be very confident; it will be close, but it probably won't be exact.
A correlation coefficient of 1 indicates a perfect positive linear relationship between the variables in the data set. When there is a strong correlation, a line of best fit can accurately represent the relationship between the variables. However, it doesn't guarantee that the predicted value will be exactly the same as the actual value.
The line of best fit provides an estimate or prediction of the unknown value based on the observed data points. While it is likely to be close to the actual value, there may still be some variability or error involved. The correlation coefficient being 1 means that the predictions are likely to be close to the actual values, but they may not be an exact match.