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 data

Calculations

x

y

y

y

2

y

y

2

y

y

2

113.0

120.5

194.3236

9.5481

290.0209

121.9

121.6

164.8656

18.9573

72.0122

128.4

139.6

26.6256

54.8488

5.0445

137.4

130.4

16.3216

108.8684

40.8832

152.5

160.1

658.4356

22.7529

436.3921

Column sums

1060.5720

214.9755

844.3529

Send data

to Excel

x

110

120

130

140

150

160

y

110

120

130

140

150

160

0

Figure1

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.)