Question

variable. \begin{tabular}{|c|r|} \hline \( \mathbf{x} \) & \multicolumn{1}{|c|}{\( \mathbf{y} \)} \\ \hline 59.2 & 75.1 \\ \hline 73.8 & 51.3 \\ \hline 48.7 & 91.6 \\ \hline 62.8 & 78.4 \\ \hline 59.7 & 87.7 \\ \hline 70.7 & 50.9 \\ \hline 67.1 & 57.6 \\ \hline 68.1 & 39 \\ \hline 78.9 & 26.1 \\ \hline 61.4 & 74.2 \\ \hline 68.1 & 47.7 \\ \hline 52.8 & 80.9 \\ \hline \end{tabular} Find the correlation coefficient and report it accurate to three decimal places. \[ r= \] \( \square \) What proportion of the variation in \( y \) can be explained by the variation in the values of \( x \) ? Report 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.) \[ r^{2}=\square \% \] \( \% \) Based on the data, calculate the regression line (each value to three decimal places) \[ y= \] \( \square \) \( x+ \) \( \square \) Predict what value (on average) for the response variable will be obtained from a value of 54.9 as the explanatory variable. Use a significance level of \( \alpha=0.05 \) to assess the strength of the linear correlation. What is the predicted response value? (Report answer accurate to one decimal place.)

          variable.
\begin{tabular}{|c|r|}
\hline \( \mathbf{x} \) & \multicolumn{1}{|c|}{\( \mathbf{y} \)} \\
\hline 59.2 & 75.1 \\
\hline 73.8 & 51.3 \\
\hline 48.7 & 91.6 \\
\hline 62.8 & 78.4 \\
\hline 59.7 & 87.7 \\
\hline 70.7 & 50.9 \\
\hline 67.1 & 57.6 \\
\hline 68.1 & 39 \\
\hline 78.9 & 26.1 \\
\hline 61.4 & 74.2 \\
\hline 68.1 & 47.7 \\
\hline 52.8 & 80.9 \\
\hline
\end{tabular}

Find the correlation coefficient and report it accurate to three decimal places.
\[
r=
\]
\( \square \)
What proportion of the variation in \( y \) can be explained by the variation in the values of \( x \) ? Report 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.)
\[
r^{2}=\square \%
\]
\( \% \)

Based on the data, calculate the regression line (each value to three decimal places)
\[
y=
\]
\( \square \) \( x+ \) \( \square \)
Predict what value (on average) for the response variable will be obtained from a value of 54.9 as the explanatory variable. Use a significance level of \( \alpha=0.05 \) to assess the strength of the linear correlation.

What is the predicted response value? (Report answer accurate to one decimal place.)

variable.

𝐱 1|c|𝐲

59.2 75.1

73.8 51.3

48.7 91.6

62.8 78.4

59.7 87.7

70.7 50.9

67.1 57.6

68.1 39

78.9 26.1

61.4 74.2

68.1 47.7

52.8 80.9

Find the correlation coefficient and report it accurate to three decimal places.

r=

□
What proportion of the variation in y can be explained by the variation in the values of x ? Report 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.)

r^2=□%

%

Based on the data, calculate the regression line (each value to three decimal places)

y=

□ x+ □
Predict what value (on average) for the response variable will be obtained from a value of 54.9 as the explanatory variable. Use a significance level of α=0.05 to assess the strength of the linear correlation.

What is the predicted response value? (Report answer accurate to one decimal place.)

Added by Peter E.

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