In order to predict y-values using the equation of a regression line, what must be true about the correlation coefficient of the variables?

A. The correlation between variables must be an x-value of a point on the graph.

B. The correlation between variables must be significant.

C. The correlation between variables must be a y-value of a point on the graph.

D. The correlation between variables must be greater than zero.

So, what does the correlation coefficient tell you about the accuracy of the regression line?

Well we only use the regression line for predictions if the regression is a reasonable fit for the data, the correlation coefficient is significant, and the data for the predicted values do not go beyond the scope of the data used to estimate the regression.

B

I agree

The correct answer is D. The correlation between variables must be greater than zero.

To understand why this is the case, let's first review what the correlation coefficient measures. The correlation coefficient, often denoted as "r", quantifies the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 represents a perfect negative linear relationship, 1 represents a perfect positive linear relationship, and 0 represents no linear relationship.

When predicting y-values using the equation of a regression line, we are essentially estimating the value of y based on a given x-value. The regression line is derived from the data points, and its equation allows us to predict any y-value for a given x-value.

However, in order for this prediction to be meaningful, there needs to be a linear relationship between the variables. If the correlation between variables is 0, it implies that there is no linear relationship between them. In this case, attempting to predict y-values based on x-values would not be accurate or meaningful.

Therefore, the correlation between variables must be greater than zero for the regression line to be a useful predictor of y-values.