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 Negative 0 point 833. Can you be confident that your predicted value will be reasonably close to the actual value? Why or why not?
No, we cannot be confident that the predicted value will be reasonably close to the actual value based on a correlation coefficient of negative 0.833.
The correlation coefficient measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where values closer to -1 or 1 indicate a stronger linear relationship, and values closer to 0 indicate a weaker relationship.
A negative correlation coefficient indicates an inverse relationship between the variables, meaning as one variable increases, the other decreases. In this case, the negative correlation coefficient of -0.833 suggests a moderately strong inverse relationship between the variables.
Since the data shows a negative correlation, the line of best fit would have a negative slope. However, making predictions outside the range of observed data becomes increasingly unreliable as the correlation coefficient approaches -1 or 1. Therefore, with a correlation coefficient of -0.833, the predicted value may not be reasonably close to the actual value due to the strength of the inverse relationship between the variables.