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 is -0.993. 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 of.
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.
I agree.
d. I can be certain that my predicted value will match the actual value exactly.
Just kidding! That would be a stretch. The correlation coefficient of -0.993 suggests a strong negative relationship between the variables. Therefore, option c. I can be very confident; it will be close, but it probably won't be exact, seems more appropriate. But remember, even with a strong correlation, there still might be some variability in the predicted value.
c. I can be very confident; it will be close, but it probably won't be exact.
c. I can be very confident; it will be close, but it probably won't be exact.
Explanation:
The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient is -0.993, which indicates a strong negative linear relationship between the variables.
A correlation coefficient close to -1 or 1 suggests a strong relationship, while a correlation coefficient close to 0 suggests a weak relationship. Since the correlation coefficient in this case is very close to -1, it means that the data points are closely clustered around the line of best fit.
Based on this strong negative relationship, we can reasonably predict that as one variable increases, the other variable will decrease, or vice versa. However, the correlation coefficient alone does not indicate the accuracy of the predicted value.
Therefore, while we can be confident that our predicted value will be close to the actual value, it may not be exact. Other factors such as scatter and variability in the data could affect the accuracy of the prediction.