How does the value of r relate to how easy it is to estimate the least-squares fit line?

The value of r, also known as the correlation coefficient, measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1.

1. If r is close to 1 or -1: This indicates a strong linear relationship between the two variables. If r is 1, it means there's a perfect positive linear relationship, and if r is -1, it means there's a perfect negative linear relationship. In these cases, it would be relatively easy to estimate the least-squares fit line because the data points are closely aligned to a clear linear trend.

2. If r is close to 0: This indicates a weak or no linear relationship between the two variables. The data points are scattered and do not align closely to any clear linear trend. In this case, it would be more difficult to estimate the least-squares fit line because the line may not provide a good fit to the data.

3. If r is exactly 0: This means there is no linear relationship between the two variables. In this case, a least-squares fit line would not be meaningful or useful for prediction.

So, the closer the absolute value of r is to 1, the easier it is to estimate the least-squares fit line. The closer it is to 0, the more difficult it is.