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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
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 Fig 1, which also displays the least-squares regression line for the data. The equation for this line is y = 0.41 + 0.89x . 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 ( 1 - 7 )- 0.9 1.2 0.0001 3.0590 3.0976 1.7 2.1 0.0313 1.0754 0.7396 2.7 3.1 0.0824 0.0216 0.0196 3.8 2.9 0.7957 0.6922 0.0036 5.2 5.5 0.213- 4.3181 5.4516 Column 1.1229 9.1663 10.3120 sums Send data to Excel Figure 1 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 |? , which for these data is v . 2. The proportion of the total variation in the sample y values that can be explained by the estimated linear relationship between x and y is |. (Round your answer to at least 2 decimal places.) 3. For the data point (5.2, 5.5), the value of the residual is . (Round your answer to at least 2 decimal places.) 4. 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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