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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 Figure 1, which also displays the least-squares regression line for the data. The equation for this line is y = - 15.46+ 1.06x . 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 ) ? 300- 223.6 211.4 103.1443 1643.8159 2570.4900 243.0 255.9 189.888 399.2004 38.4400 263.0 247.1 263.088 1.4884 225.0000 276.8 301.3 545.3159 251.1591 1536.6400 303.2 294.8 123.9214 1921.2442 1069.2900 Column 1225.3585 4216.9081 5439.8600 sums 230 240 260 280 300 320 Send data to Excel Figure 1 Answer the following: 1. For the data point (263.0, 247.1), the value of the residual is . (Round your answer to at least 2 decimal places.) 2. The total variation in the sample y values is given by the |? which for these data is |? 3. 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.) 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 ? v, which for these data is |
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