Bivariate data obtained for the paired variables x and y are shown, in the table labelled "Sample data". These data are plotted in the scatter plot in the figure, which also displays the least-squares regression for the data. The equation for this line is

^y=50.97−0.96x.

In the "Calculations" table are calculations involving the observed y values, the mean ¯y
of these values, and the values ^y

predicted from the regression equation.

Sample data
x y
21.7 32.2
23.7 29.8
25.6 24.3
27.6 26.1
30.5 22.1

Calculations

(y−¯y)2(y−^y)2(^y−¯y)237.21004.251816.30540.09005.84674.48893.24001.29800.44350.00002.34082.340915.0000.155119.4461

1) Choose the best answer.

The total variation in the sample y values is given by the (a) error sum of squares (b) total sum of squares (c) regression sum of squares

which for these data is (a) 43.0239 (b) 13.8935 (c) 56.5400.

2) The value r2
is the proportion of the total variation in the sample y values that is explained by the estimated linear relationship between x and y. For these data, what is the value of r2?

3) For the data point (23.7, 25.8), what is the value of the residual?

4) The least-squares regression line given above is said to be a line which "best fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the _____
for these data is _____.