Bivariate data obtained for the paired variables x and y are shown below, in the table labeled "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 = 2.46+0.91x.
^
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
(-)²
(-)
(ー)
21.8
21.2
14.4552
1.2056
24.0100
23.6
26.1
4.6829
4.6829
0.0000
26.4 25.3
0.1475
1.4019
0.6400
28.4
26.9
4.8576
1.9712
0.6400
30.3 31.0
15.4685
0.9351
24.0100
Column sum:
39.6117
Column sum:
10.1967
Column sum:
49.3000
Figure 1
Answer the following.
(a) The least-squares regression line given above is said to be a line that "best fits" the sample data. The term "best
fits" is used because the line has an equation that minimizes the (Choose one)
data is (Choose one) ▼
(b) The total variation in the sample y-values is given by the (Choose one)
(Choose one) ▼
▼, which for these
▼, which for these data is
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