Question

Espanol 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 \( \hat{y}=126.40-0.92 x \). 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 \( \boldsymbol{x} \) & \( \boldsymbol{y} \) \\ \hline 54.0 & 76.0 \\ \hline 61.0 & 75.5 \\ \hline 64.2 & 61.9 \\ \hline 71.4 & 63.7 \\ \hline 76.2 & 55.5 \\ \hline \\ \hline Send data to Excel \\ \hline \end{tabular} Calculations \begin{tabular}{|c|c|c|} \hline\( (y-\bar{y})^{2} \) & \( (\hat{y}-\vec{y})^{2} \) & \( (y-\hat{y})^{2} \) \\ \hline 89.8704 & 104.0400 & 0.5184 \\ \hline 80.6404 & 14.1376 & 27.2484 \\ \hline 21.3444 & 0.6659 & 29.5501 \\ \hline 7.9524 & 33.7329 & 8.9281 \\ \hline 121.4404 & 104.5302 & 0.6336 \\ \hline \begin{tabular}{c} Column sum: \\ 321.2480 \end{tabular} & \begin{tabular}{c} Column sum: \\ 257.1065 \end{tabular} & \begin{tabular}{c} Column sum: \\ 66.8787 \end{tabular} \\ \hline \end{tabular} Answer the following. (a) 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) \( \quad \), which for these data is (Choose one) \( \nabla \). (b) The variation in the sample \( y \)-values that is explained by the estimated linear relationship between \( x \) and \( y \) is given by the (Choose one) \( \nabla \), which for these data is (Choose one) \( \nabla \). (c) 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 \( \square \). (Round your answer to at least 2 decimal places.)

          Espanol
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 \( \hat{y}=126.40-0.92 x \).

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 \( \boldsymbol{x} \) & \( \boldsymbol{y} \) \\
\hline 54.0 & 76.0 \\
\hline 61.0 & 75.5 \\
\hline 64.2 & 61.9 \\
\hline 71.4 & 63.7 \\
\hline 76.2 & 55.5 \\
\hline \\
\hline Send data to Excel \\
\hline
\end{tabular}

Calculations
\begin{tabular}{|c|c|c|}
\hline\( (y-\bar{y})^{2} \) & \( (\hat{y}-\vec{y})^{2} \) & \( (y-\hat{y})^{2} \) \\
\hline 89.8704 & 104.0400 & 0.5184 \\
\hline 80.6404 & 14.1376 & 27.2484 \\
\hline 21.3444 & 0.6659 & 29.5501 \\
\hline 7.9524 & 33.7329 & 8.9281 \\
\hline 121.4404 & 104.5302 & 0.6336 \\
\hline \begin{tabular}{c} 
Column sum: \\
321.2480
\end{tabular} & \begin{tabular}{c} 
Column sum: \\
257.1065
\end{tabular} & \begin{tabular}{c} 
Column sum: \\
66.8787
\end{tabular} \\
\hline
\end{tabular}

Answer the following.
(a) 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) \( \quad \), which for these data is (Choose one) \( \nabla \).
(b) The variation in the sample \( y \)-values that is explained by the estimated linear relationship between \( x \) and \( y \) is given by the (Choose one) \( \nabla \), which for these data is (Choose one) \( \nabla \).
(c) 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 \( \square \). (Round your answer to at least 2 decimal places.)

Espanol
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=126.40-0.92 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

x y

54.0 76.0

61.0 75.5

64.2 61.9

71.4 63.7

76.2 55.5

Send data to Excel

Calculations

(y-y̅)^2 (ŷ-y⃗)^2 (y-ŷ)^2

89.8704 104.0400 0.5184

80.6404 14.1376 27.2484

21.3444 0.6659 29.5501

7.9524 33.7329 8.9281

121.4404 104.5302 0.6336

Column sum:

321.2480

Column sum:

257.1065

Column sum:

66.8787

Answer the following.
(a) 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) ∇.
(b) The variation in the sample y-values that is explained by the estimated linear relationship between x and y is given by the (Choose one) ∇, which for these data is (Choose one) ∇.
(c) 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.)

Added by Tyesha T.

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