Linear Regression
Use linear regression to find the equation for the linear function that best fits this data. Round both numbers to two decimal places. Write your final answer in a form of an equation $y=m x+b$
\begin{tabular}{|r|r|r|r|r|r|r|}
\hline$x$ & 1 & 2 & 3 & 4 & 5 & 6 \\
\hline$y$ & 79 & 100 & 110 & 127 & 149 & 165 \\
\hline
\end{tabular}

Step 1 ：We are given the following data points: \(x = [1, 2, 3, 4, 5, 6]\) and \(y = [79, 100, 110, 127, 149, 165]\).

Step 2 ：We need to find the equation of the line that best fits these data points. The equation of a line is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Step 3 ：We can use the formulas for the slope (\(m\)) and y-intercept (\(b\)) in a linear regression, which are given by: \[m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}\] and \[b = \frac{(\sum y) - m(\sum x)}{n}\]

Step 4 ：First, we calculate the necessary sums from the given data: \(n = 6\), \(\sum x = 21\), \(\sum y = 730\), \(\sum xy = 2852\), and \(\sum x^2 = 91\).

Step 5 ：Substituting these values into the formulas, we find \(m = 16.97142857142857\) and \(b = 62.26666666666667\).

Step 6 ：Rounding these values to two decimal places, we get \(m = 16.97\) and \(b = 62.27\).

Step 7 ：\(\boxed{\text{Final Answer: The equation for the linear function that best fits the data is } y = 16.97x + 62.27}\)