The problem asks for a linear regression to find the equation of the linear function that best fits the given data, rounding the parameters to two decimal places.

Data points:

• $x = [1, 2, 3, 4, 5, 6]$
• $y = [814, 1037, 1192, 1457, 1891, 2244]$

We need to use the formula for the linear regression equation, which is: $y = mx + b$ where:

• $m$ is the slope,
• $b$ is the y-intercept.

The slope $m$ and intercept $b$ can be computed using the following formulas: $m = \frac{n(\sum{xy}) - (\sum{x})(\sum{y})}{n(\sum{x^2}) - (\sum{x})^2}$ $b = \frac{\sum{y} - m(\sum{x})}{n}$ where $n$ is the number of data points.

Let me calculate these values for you.The linear equation that best fits the given data using linear regression is:

$y = 285.06x + 441.47$

Let me know if you need further details or explanations. Here are some related questions to deepen your understanding:

1. How is the linear regression formula derived?
2. What is the significance of the slope and y-intercept in the linear equation?
3. Can you explain how linear regression works in machine learning?
4. How can we measure the accuracy of a linear regression model?
5. What are some common applications of linear regression in real-world data analysis?

Tip: Always plot your data along with the regression line to visually assess the fit!