The white forehead patch of the male collared flycatcher is important in mate attraction. Griffith and Sheldon (2001) found that the length of the patch varied from year to year. They measured the forehead patch on a sample of 30 males in two consecutive years, 1998 and 1999, on the Swedish island of Gotland. The scatter plot provided gives the pair of measurements for each male. The solid regression line predicts the 1999 measurement from the 1998 measurement. The dashed line is drawn through the means for 1998 and 1999, but it has a slope of one. The difference between the two lines indicates that males with the longest patches in 1998 had smaller patches in 1999, relative to the other birds. Similarly, the males with the smallest patches in 1998 had larger patches, on average, in 1999, relative to other birds.

a. The following table summarizes the data. Use these numbers to calculate the regression slope.

b. Now let the patch length in 1998 be the response variable (Y) . Use the patch length in 1999 to predict patch length in 1998. What is the slope of this new regression?

c. What is the most likely reason that the slope is less than one in both regressions?

Transcribed Image Text:

Patch length 1999 (mm) 11 10- 8 5 5 6 7 8 9 Patch length 1998 (mm) 10 11