Problem Page

Bivariate data obtained for the paired variables x

and y

are shown below, in the table labelled “Sample data.” These data are plotted in the scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is =

y

+

8.93

0.96

x

.

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 dataCalculationsxy?yy2?yy2?yy2Column sums Send datato Excel    x110120130140150160y1101201301401501600 Figure 1

Answer the following:

1. For the data point (128.4, 139.6), the value of the residual is

. (Round your answer to at least 2 decimal places.)

2. 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

?

total sum of squares

regression sum of squares

error sum of squares

, which for these data is

?

1060.5720

844.3529

214.9755

.

3. The total variation in the sample y values is given by the

?

total sum of squares

regression sum of squares

error sum of squares

, which for these data is

?

1060.5720

844.3529

214.9755

.

4. The value r

2

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, the value of r

2

is

. (Round your answer to at least 2 decimal places.)