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 . Can you be confident that your predicted value will be reasonably close to the actual value? Why or why not?m
The correlation coefficient alone is not sufficient to determine whether the predicted value will be reasonably close to the actual value. The correlation coefficient only measures the strength and direction of the linear relationship between two variables, but it does not indicate the accuracy of predictions.
To assess the accuracy of predictions, other factors need to be considered, such as the variability of the data points around the line of best fit, the sample size, and the presence of outliers. Additionally, it is important to validate the predictive model using different statistical methods and performance metrics.
So, based solely on the correlation coefficient value, it is not possible to determine if the predicted value will be reasonably close to the actual value. Further analysis and evaluation of the data and the predictive model are necessary to make a more confident statement.