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gin - Search ALEKS A ALEKS - Renonia Bruce -Learn V/alekscgi/x/Isl.exe/1o_u-IgNs|kr7j8P3jH-Iv-6txjbonmDn7WsVrRAXK6XnHkiR... Cormstntion and Simple Linem Regression Simple linear regression: Explained and unexplained variation Reno 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 \( \hat{y}=5.24-0.62 x \). 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|c|c|c|} \hline \multicolumn{2}{|c|}{ Sample data } & \multicolumn{2}{|l|}{ Calculations } & \multirow{3}{}{\( (y-\hat{y})^{2} \)} \\ \hline \( \boldsymbol{x} \) & \( y \) & \( (0-\bar{n})^{2} \) & \( \hat{(\hat{}-)^{2}} \) & \\ \hline 0.7 & 4.7 & & \( (y-y) \) & \\ \hline 2.2 & 4.5 & 1.8496 & 2.1492 & 0.0112 \\ \hline 29 & 28 & 1.3456 & 0.2873 & 0.3894 \\ \hline 4.2 & 2.6 & 0.2916 & 0.0104 & 0.4122 \\ \hline 5.2 & 21 & 0.5476 & 0.4956 & 0.0013 \\ \hline \multirow{2}{*}{\multicolumn{2}{|c|}{ Send data to Excell }} & 1.5376 & 1.7530 & 0.0071 \\ \hline & & \begin{tabular}{l} Column sum: \\ 5.5720 \end{tabular} & \begin{tabular}{l} Column sum: \\ 4.6954 \end{tabular} & \begin{tabular}{l} Column sum: \\ 0.8211 \end{tabular} \\ \hline \end{tabular} Answer the following. (a) The variation in the sample \( y \)-values that is not explained by the estimated linear relationship between \( x \) and \( y \) is given by the (Choose one) \( \square \) , which for these data is \( \square \) (b) The value \( r^{2} \) 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 of \( r^{2} \) is \( \square \). (Round your answer to at least 2 decimal places.) (c) The least-squares regression line given above is said to be a line that "best fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the (Choose one) which for these data is (Choose one) \( \mathbf{~} \). Explanation Check

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A ALEKS - Renonia Bruce -Learn
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Cormstntion and Simple Linem Regression
Simple linear regression: Explained and unexplained variation
Reno
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 \( \hat{y}=5.24-0.62 x \).
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|c|c|c|}
\hline \multicolumn{2}{|c|}{ Sample data } & \multicolumn{2}{|l|}{ Calculations } & \multirow{3}{*}{\( (y-\hat{y})^{2} \)} \\
\hline \( \boldsymbol{x} \) & \( y \) & \( (0-\bar{n})^{2} \) & \( \hat{(\hat{*}-)^{2}} \) & \\
\hline 0.7 & 4.7 & & \( (y-y) \) & \\
\hline 2.2 & 4.5 & 1.8496 & 2.1492 & 0.0112 \\
\hline 29 & 28 & 1.3456 & 0.2873 & 0.3894 \\
\hline 4.2 & 2.6 & 0.2916 & 0.0104 & 0.4122 \\
\hline 5.2 & 21 & 0.5476 & 0.4956 & 0.0013 \\
\hline \multirow{2}{*}{\multicolumn{2}{|c|}{ Send data to Excell }} & 1.5376 & 1.7530 & 0.0071 \\
\hline & & \begin{tabular}{l} 
Column sum: \\
5.5720
\end{tabular} & \begin{tabular}{l} 
Column sum: \\
4.6954
\end{tabular} & \begin{tabular}{l} 
Column sum: \\
0.8211
\end{tabular} \\
\hline
\end{tabular}

Answer the following.
(a) The variation in the sample \( y \)-values that is not explained by the estimated linear relationship between \( x \) and \( y \) is given by the (Choose one) \( \square \) , which for these data is \( \square \)
(b) The value \( r^{2} \) 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 of \( r^{2} \) is \( \square \). (Round your answer to at least 2 decimal places.)
(c) The least-squares regression line given above is said to be a line that "best fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the (Choose one) which for these data is (Choose one) \( \mathbf{~} \).
Explanation
Check

gin - Search
ALEKS
A ALEKS - Renonia Bruce -Learn
V/alekscgi/x/Isl.exe/1ou-IgNs|kr7j8P3jH-Iv-6txjbonmDn7WsVrRAXK6XnHkiR...
Cormstntion and Simple Linem Regression
Simple linear regression: Explained and unexplained variation
Reno
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 ŷ=5.24-0.62 x.
In the "Calculations" table are calculations involving the observed y-values, the mean y̅ of these values, and the values ŷ predicted from the regression equation.

2|c| Sample data 2|l| Calculations 3*(y-ŷ)^2

x y (0-n̅)^2 (̂*̂̂̂-̂)̂^̂2̂

0.7 4.7 (y-y)

2.2 4.5 1.8496 2.1492 0.0112

29 28 1.3456 0.2873 0.3894

4.2 2.6 0.2916 0.0104 0.4122

5.2 21 0.5476 0.4956 0.0013

2*2|c| Send data to Excell 1.5376 1.7530 0.0071

Column sum:

5.5720

Column sum:

4.6954

Column sum:

0.8211

Answer the following.
(a) The variation in the sample y-values that is not explained by the estimated linear relationship between x and y is given by the (Choose one) □ , which for these data is □
(b) The value r^2 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 of r^2 is □. (Round your answer to at least 2 decimal places.)
(c) The least-squares regression line given above is said to be a line that "best fits" the sample data. The term "best fits" is used because the line has an equation that minimizes the (Choose one) which for these data is (Choose one) .
Explanation
Check

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