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 -0.833. Can you be confident that your predicted value will be reasonably close to the actual value? Why or why
not?
No, I cannot be confident that the predicted value will be reasonably close to the actual value based solely on the correlation coefficient of -0.833. The correlation coefficient measures the strength and direction of the linear relationship between the variables, but it does not provide information about the accuracy or precision of predictions made using the line of best fit.
Other factors such as the variability of the data, the sample size, and the presence of outliers also need to be taken into consideration. Additionally, it is important to assess the residual plot and conduct hypothesis testing to determine the statistical significance of the relationship between the variables.
Therefore, while the negative correlation coefficient suggests an inverse relationship between the variables, more analysis and evaluation is needed to determine the reliability of the prediction made using the line of best fit.