The figure below gives data on solar radiation SRD and conce

The figure below gives data on solar radiation (SRD) and concentration of dimethylsulfide (DMS) over a region of the Mediterranean. The correlation is

r = 0.969.

Explain in simple language why knowing only these correlations enables you to say that prediction of DMS from SRD by a regression line will be much more accurate than prediction of a golfer\'s second-round score from his first-round score. (Select all that apply.)

1. The fraction of the variation in the observed values of y explained by the least-squares regression of y on x is given by r. The higher this fraction, the less likely that the prediction is accurate.

2. The fraction of the variation in the observed values of y explained by the least-squares regression of y on x is given by r². The higher this fraction, the more likely that the prediction is accurate.

3. The fraction of the variation in the observed values of x explained by the least-squares regression of y on x is given by r². The higher this fraction, the more likely that the prediction is accurate.

4. The fraction of the variation in the observed values of y explained by the least-squares regression of y on x is given by r². The higher this fraction, the less likely that the prediction is accurate.

5. When r is closer to 1 or 1, the points in the scatterplot fall closer to the regression line, therefore predictions based on this line are more accurate.

Solution

Option (2) is correct and self explanatory.

Option (5) is also correct.