Explain why it is desirable to have r2 large and se small

Question

Both r² and se are used to assess the fit of a line.

a. Is it possible that both r² and se could be large for a bivariate data set? Explain. (A picture might be helpful.)

b. Is it possible that a bivariate data set could yield values of r² and se that are both small? Explain. (Again, a picture might be helpful.)

c. Explain why it is desirable to have r² large and se small if the relationship between two variables x and y is to be described using a straight line.