The following table lists the birth weights (in pounds), $x$, and the lengths (in inches), $y$, for a set of newborn babies at a local hospital. \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{8}{|c|}{ Birth Weights and Lengths } \\ \hline \begin{tabular}{c} Birth Weight \\ (in Pounds), $x$ \end{tabular} & 9 & 6 & 6 & 10 & 9 & 10 & 7 & 4 & 3 & 11 \\ \hline \begin{tabular}{c} Length (in \\ Inches), $y$ \end{tabular} & 21 & 17 & 18 & 21 & 21 & 19 & 19 & 17 & 16 & 20 \\ \hline \end{tabular} Copy Data Step 2 of 2 : Predict the length of a 9-pound baby. Assume the regression equation is appropriate for prediction. Round your answer to two decimal places, if necessary.

Step 1 ：Given the birth weights (in pounds), $x$, and the lengths (in inches), $y$, for a set of newborn babies at a local hospital, we are asked to predict the length of a 9-pound baby. The data is as follows: $x = [ 9, 6, 6, 10, 9, 10, 7, 4, 3, 11]$ and $y = [21, 17, 18, 21, 21, 19, 19, 17, 16, 20]$. The number of data points, $n$, is 10.

Step 2 ：We need to find the linear regression equation that best fits the given data. The general form of a linear regression equation is $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept.

Step 3 ：The slope, $m$, can be calculated as $\frac{n(\Sigma xy) - (\Sigma x)(\Sigma y)}{n(\Sigma x^2) - (\Sigma x)^2}$. After calculating, we find that $m = 0.5939849624060151$.

Step 4 ：The y-intercept, $b$, can be calculated as $\frac{(\Sigma y) - m(\Sigma x)}{n}$. After calculating, we find that $b = 14.445112781954887$.

Step 5 ：Once we have the equation, we can substitute $x = 9$ into the equation to predict the length of a 9-pound baby. The predicted length is approximately 19.790977443609023 inches.

Step 6 ：Final Answer: The predicted length of a 9-pound baby is approximately \(\boxed{19.79}\) inches.