Given a data set with two dimensions X and Y: (a) Use a linear regression method to calculate the parameters α and β where y = α + β x. (b) Estimate the quality of the model obtained in (a) using the...

Given a data set with two dimensions X and Y:

(a) Use a linear regression method to calculate the parameters α and β where y = α + β x.

(b) Estimate the quality of the model obtained in (a) using the correlation coefficient r.

(c) Use an appropriate nonlinear transformation (one of those represented in Table 5.3 ) to improve regression results. What is the equation for a new, improved, and nonlinear model? Discuss a reduction of the correlation coeffi cient value.

Table 5.3