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 \( \hat{y}=-33.68+1.12 x \). In the "Calculations" table are calculations involving the observed \( y \)-values, the mean \( \bar{y} \) of these values, and the values \( \hat{y} \) predicted from the regression equation. \begin{tabular}{|c|c|} \hline \multicolumn{2}{|c|}{ Sample data } \\ \hline\( x \) & \( y \) \\ \hline 214.7 & 211.7 \\ \hline 244.4 & 251.9 \\ \hline 265.6 & 244.4 \\ \hline 278.0 & 269.2 \\ \hline 302.5 & 321.4 \\ \hline \end{tabular} Send data to Excel \begin{tabular}{l} Calculations \\ \begin{tabular}{|c|c|c|} \hline\( (\boldsymbol{y}-\overline{\boldsymbol{y}})^{\mathbf{2}} \) & \( (\hat{\boldsymbol{y}}-\overline{\boldsymbol{y}})^{\mathbf{2}} \) & \( (\boldsymbol{y}-\hat{\boldsymbol{y}})^{\mathbf{2}} \) \\ \hline 2305.9204 & 2802.2201 & 24.1671 \\ \hline 61.1524 & 386.9876 & 140.4699 \\ \hline 234.7024 & 16.5812 & 376.0497 \\ \hline 89.8704 & 322.5616 & 71.9104 \\ \hline 3804.4224 & 2061.1600 & 265.0384 \\ \hline Column sum: & Column sum: & Column sum: \\ \hline 6496.0680 & 5589.5105 & 877.6354 \\ \hline \end{tabular} \\ \hline \end{tabular} Figure 1 Answer the following. Explanation Check ) 2024 McGraw Hill LLC. All Rights Reserved. Terms of Use I Privacy Center I A Type here to search
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- The table "Sample data" provides pairs of \( x \) and \( y \) values. - The regression equation given is \( \hat{y} = -33.68 + 1.12x \). This equation predicts \( y \) based on \( x \). Show more…
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Bivariate data obtained for the paired variables 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 = 15.61 + 0.89x. In the "Calculations" table, there are calculations involving the observed values, the mean of these values, and the values predicted from the regression equation. Sample data: x y -y y^2 108.2 110.8 1.2277 406.1031 118.2 127.7 47.4997 126.6075 133.0 123.7 105.6784 3.6864 141.9 145.3 11.5532 96.8453 151.5 152.8 5.5460 338.0082 Column sums: 171.5050 971.2505 1146.3320 Figure 1: Scatter plot of the sample data with the least-squares regression line.
Sri K.
Stat: Need someone to explain this to me please?
Paul A.
Run a regression analysis on the following bivariate set of data with y as the response variable: 54.2 51.2 60.9 55.4 104.3 35.5 4.7 3.4 133.8 31.8 35.1 71.2 56.3 13.7 45.1 -1.9 72.2 41.1 14.1 43.1 34.3 29.5 Find the correlation coefficient and report it accurately to three decimal places. What proportion of the variation in y can be explained by the variation in the values of x? Report the answer as a percentage accurate to one decimal place. (If the answer is 0.84471, then it would be 84.5%. You would enter 84.5 without the percent symbol.) Based on the data, calculate the regression line (each value to three decimal places). Predict what value (on average) for the response variable will be obtained from a value of 62.5 as the explanatory variable. Use a significance level of 0.05 to assess the strength of the linear correlation. What is the predicted response value? (Report the answer accurately to one decimal place: y = )
Madhur L.
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