Note: Your teacher will grade your responses to the follow questions to ensure you receive proper credit for your answers. 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?
Yes, you can be confident that the predicted value will be reasonably close to the actual value, to some extent. The correlation coefficient, -0.833, indicates a moderately strong negative linear relationship between the variables in the data set. This means that as one variable increases, the other variable tends to decrease. The line of best fit, derived from the data, represents this relationship.
When making a prediction using the line of best fit, the value obtained will likely not match the actual value exactly, but it should be reasonably close. The fact that the correlation coefficient is not equal to -1 or +1 suggests that there is some variation or error in the prediction. However, the closer the correlation coefficient is to -1 (or +1), the stronger the linear relationship between the variables, and therefore, the more confidence you can have in the accuracy of the prediction.
In this case, with a correlation coefficient of -0.833, there is a reasonably strong negative linear relationship between the variables, indicating that the predicted value should be reasonably close to the actual value. However, it is important to note that the correlation coefficient alone does not guarantee the accuracy of the prediction, as other factors like outliers, sample size, and underlying assumptions of the data should also be considered.