(a) The variation in the sample y values that is explained by the estimated linear relationship between x and y is given by the ? which for these data is 2 (b) The value ris 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 is|. (Round your answer to at least 2 decimal places.) (c) 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 ? , which for these data is ?

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(a) The variation in the sample y values that is explained by the estimated linear relationship
between x and y is given by the ?
which for these data is
(b) The value r 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
2
of r is . (Round your answer to at least 2 decimal places.)
(c) 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 ?
v, which for these data is ?
Transcribed Image Text:(a) The variation in the sample y values that is explained by the estimated linear relationship between x and y is given by the ? which for these data is (b) The value r 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 2 of r is . (Round your answer to at least 2 decimal places.) (c) 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 ? v, which for these data is ?
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
%3D
scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is y = 2.90+0.98x .
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
80+
y
75+
y-y.
0.2601
y-y
y.
55.5
57.8
90.0601
80.6404
70-
60.6
60.8
2.2141
20.1781
35.7604
55+
65.6
69.8
6.8225
0.1665
9.1204
50+
68.5
67.7
5.4289
10.5625
0.8464
55+
76.0
77.8
0.1764
112.3600
121.4404
50+
Column
14.9021
233.3271
247.8080
sums
50
55
60
65
70
75
80
Send data to Excel
Figure 1
Transcribed Image Text: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 %3D scatter plot in Figure 1, which also displays the least-squares regression line for the data. The equation for this line is y = 2.90+0.98x . 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 80+ y 75+ y-y. 0.2601 y-y y. 55.5 57.8 90.0601 80.6404 70- 60.6 60.8 2.2141 20.1781 35.7604 55+ 65.6 69.8 6.8225 0.1665 9.1204 50+ 68.5 67.7 5.4289 10.5625 0.8464 55+ 76.0 77.8 0.1764 112.3600 121.4404 50+ Column 14.9021 233.3271 247.8080 sums 50 55 60 65 70 75 80 Send data to Excel Figure 1
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