Annual high temperatures in a certain location have been tracked for several years. Let $X$ represent the year and $Y$ the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places). \[ y=\square x+\square \] \begin{tabular}{|r|r|} \hline$x$ & $y$ \\ \hline 2 & 37.04 \\ \hline 3 & 34.88 \\ \hline 4 & 33.92 \\ \hline 5 & 30.66 \\ \hline 6 & 28.6 \\ \hline 7 & 26.94 \\ \hline 8 & 23.68 \\ \hline 9 & 18.92 \\ \hline 10 & 19.46 \\ \hline 11 & 16.4 \\ \hline \end{tabular} Question Help: Video Submit Question

Step 1 ：Let \( n \) be the number of data points, \( x \) and \( y \) be the individual data points, and \( \Sigma \) represent the sum of the values.

Step 2 ：Given data points for \( x \) are [2, 3, 4, 5, 6, 7, 8, 9, 10, 11] and for \( y \) are [37.04, 34.88, 33.92, 30.66, 28.6, 26.94, 23.68, 18.92, 19.46, 16.4].

Step 3 ：Calculate the sum of \( x \) values, \( \Sigma x = 65 \).

Step 4 ：Calculate the sum of \( y \) values, \( \Sigma y = 270.5 \).

Step 5 ：Calculate the sum of \( x \times y \) values, \( \Sigma xy = 1562.60 \).

Step 6 ：Calculate the sum of \( x^2 \) values, \( \Sigma x^2 = 505 \).

Step 7 ：Use the formula for the slope \( m \) of the regression line: \( m = \frac{n(\Sigma xy) - (\Sigma x)(\Sigma y)}{n(\Sigma x^2) - (\Sigma x)^2} \).

Step 8 ：Substitute the known values into the slope formula to get \( m = \frac{10(1562.60) - (65)(270.5)}{10(505) - (65)^2} \).

Step 9 ：Calculate the slope \( m = -2.37 \).

Step 10 ：Use the formula for the y-intercept \( b \) of the regression line: \( b = \frac{\Sigma y - m(\Sigma x)}{n} \).

Step 11 ：Substitute the known values into the y-intercept formula to get \( b = \frac{270.5 - (-2.37)(65)}{10} \).

Step 12 ：Calculate the y-intercept \( b = 42.46 \).

Step 13 ：Write the final regression line equation as \( y = -2.37x + 42.46 \).

Step 14 ：Box the final answer: \( y = \boxed{-2.37}x + \boxed{42.46} \)