Find the linear regression line for the following table of values. You will need to use a calculator, spreadsheet, or statistical software.

Enter your answer in the form y=mx+b, with m and b both rounded to two decimal places.

x
y
1
3.1
2
4.37
3
5.5
4
5.29
5
7.52
6
8.31
7
9.01

To find the linear regression line, we need to determine the line of best fit in the form:

\[
y = mx + b
\]

where:
- \(m\) is the slope of the line.
- \(b\) is the y-intercept.

We use the formulas for calculating the slope \(m\) and y-intercept \(b\) of the regression line:

\[
m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}
\]

\[
b = \frac{(\sum y)(\sum x^2) - (\sum x)(\sum xy)}{n(\sum x^2) - (\sum x)^2}
\]

where:
- \(n\) is the number of data points.
- \(\sum x\), \(\sum y\), \(\sum xy\), and \(\sum x^2\) are the summations of the respective quantities.

Let's compute these values.The linear regression line for the given data, rounded to two decimal places, is:

\[
y = 0.99x + 2.21
\]

If you have any questions or would like more details on the calculation, please let me know!

### Related Questions:
1. How do you interpret the slope and intercept of a linear regression line?
2. What is the correlation coefficient, and how does it relate to the regression line?
3. How would the regression line change if one of the data points were different?
4. What are some applications of linear regression in real-world scenarios?
5. How can you use a spreadsheet tool like Excel to find a regression line?

**Tip:** Always visualize the data points and the regression line to check the fit visually!

Learn how to find the linear regression line for a set of data points using statistical methods. This problem involves calculating the slope and y-intercept of the regression line. The solution provides detailed steps and formulas to derive the equation y = 0.99x + 2.21 from the given data points.

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