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?
Responses
I can be very confident; it will be very close, but it probably won’t be exact.
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.
I can be certain that my predicted value will match the actual value exactly.
I can be very confident; it will be very close, but it probably won’t be exact.
why
The correlation coefficient is a measure of the strength and direction of the relationship between two variables. A correlation coefficient of -1 indicates a perfect negative linear relationship between the variables. This means that as one variable increases, the other variable decreases in a perfectly predictable manner.
Using a line of best fit, which represents this negative relationship, allows for reasonably accurate predictions. However, it's important to note that the predicted value may not be exact due to potential errors or variability in the data. Hence, while there is a high level of confidence in the prediction being close to the actual value, it is unlikely to be an exact match.