https://file.aiquickdraw.com/mathbot/file/1728446674374fqh50d5w.jpg

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!

Use linear regression to find the equation for the linear function that best fits this data. Round parameters to two decimal places. Data: x = [1, 2, 3, 4, 5, 6], y = [814, 1037, 1192, 1457, 1891, 2244].

Find the linear regression equation for the given data points (x = [1, 2, 3, 4, 5, 6], y = [814, 1037, 1192, 1457, 1891, 2244]). Learn how to calculate the slope and y-intercept using algebraic formulas and rounding the results to two decimal places.

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