Bivariate data
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Bivariate data obtained for the paired variables and 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 .
In the "Calculations" table are calculations involving the observed values, the mean of these values, and the values predicted from the regression equation.
Sample data
X Y
56.3 58.2
60.6 60.1
66.1 65.7
68.6 64.7
75.7 77.0
Calculations
- 2 ^ - 2 - 2
(y - y) (y - y) (y - y)
2.0678 70.1909 48.1636
0.4956 18.8009 25.4016
0.0751 0.6956 0.3136
13.1334 10.1379 0.1936
4.0080 97.1802 140.6596
19.7799 197.0054 214.7320
Answer the following:
1. The variation in the sample y values that is explained by the estimated linear relationship between x and y is given by the ____
a. Regression sum of squares
b. error sum of squares
c. total sum of squares
which for these data is ___
a. 197.0054
b. 214.7320
c. 19.7799
2. The proportion of the total variation in the sample y values can be explained by the estimated linear relationship between x and y is___ (Round your answer to at least two decimal places.)
3. 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 ___
a. regression sum of squares
b. error sum of squares
c. total sum of squares
which for these data is ___
a. 197.0054
b. 214.7320
c. 19.7799
4. For the data point (56.3, 58.2), the value of the residual is ___ (Round your answer to at least two decimal places.)
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