Question

Suppose a doctor measures the height x, and head circumference, y, of 8 children and obtains the data below. The correlation coefficient is 0.807 and the least squares regression line is y=0.159x + 13.050. Complete parts (a) through (c) below. Height, x 27.5 25.5 26.25 25.75 27.25 26.5 26 26.75 27.25 27.25 26.75 Head Circumference, y 17.4 172 17.1 17.1 17.4 17.3 17.1 174 173 174 17.4 (a) Compute the coefficient of determination, R2 R-% (Round to one decimal place as needed.)

Answer 1

Solution :

Suppose we fit a simple linear least sqaure regression to predict response variable, y based on the regressor, x. We know the coefficient of correlation, r. Then coefficient of determination R^2 (R-squared) is given by, R-squared = r^2.

In this case, r = 0.807. So coefficient of determination, R-squared = 0.807^2 = 0.651 or 65.1%.