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, you cannot be confident that your 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 two variables. In this case, a coefficient of -0.833 indicates a strong negative linear relationship. However, it does not provide information about the accuracy of predictions made using the line of best fit.
To determine the reliability of predictions, you should consider other factors such as the variability of the data points around the line of best fit, the sample size, and any potential outliers or influential observations. Additionally, it is crucial to assess the overall fit of the linear model using techniques like residual analysis and hypothesis testing.