You use a line best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is .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.
*** = my answer
Agree with your answer.
Correlation coefficient of 0.793 is positive, but not strong.
Follow following link to get a visual interpretation.
https://www.mathsisfun.com/data/correlation.html
B. I can be a little confident; it might be close, or it might be way off.
The correlation coefficient is a measure of the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient is 0.793. The correlation coefficient ranges from -1 to 1.
A value of 1 indicates a perfect positive linear relationship, where all data points fall perfectly on a straight line. In this case, you would be certain that your predicted value would match the actual value exactly.
A value of -1 indicates a perfect negative linear relationship, where all data points fall perfectly on a straight line, but with a negative slope. Again, you would be certain that your predicted value would match the actual value exactly.
A value of 0 indicates no linear relationship between the variables. In this case, using a line of best fit to make predictions would not be meaningful, and you cannot be confident in the accuracy of your predicted value.
The correlation coefficient of 0.793 suggests a moderate to strong positive linear relationship, but not a perfect one. This means that there is some degree of predictability in the data, but there may still be some variability in the relationship. Therefore, you can be a little confident that your predicted value will be reasonably close to the actual value, but there is still a possibility of some deviation.