The figure below gives data on solar radiation (SRD) and concentration of dimeth

Question

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.

Explanation / Answer

Option (2) is correct and self explanatory.

Option (5) is also correct.

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