Using a calculator or statistical software, find the linear regression line for the data in the table below.

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

x 

 y 

1

3.53

2

4.93

3

1.58

4

2.72

5

4.68

6

3.34

To find the linear regression line for the given data, we will use the same formulas for the slope \(m\) and the 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:
- \(x = [1, 2, 3, 4, 5, 6]\)
- \(y = [3.53, 4.93, 1.58, 2.72, 4.68, 3.34]\)

Let's compute the values to find \(m\) and \(b\).The linear regression line for the given data, rounded to two decimal places, is:

\[
y = -0.02x + 3.52
\]

If you have any further questions or need more details, feel free to ask!

### Related Questions:
1. What does a negative slope indicate about the relationship between \(x\) and \(y\)?
2. How can you assess the accuracy of a regression line?
3. What is the difference between linear and non-linear regression?
4. How would you calculate the coefficient of determination (R-squared) for this regression?
5. What are some common pitfalls in interpreting regression results?

**Tip:** When the slope is close to zero, it suggests a weak relationship between \(x\) and \(y\).

Learn how to find the linear regression line for a dataset using a calculator or statistical software. This problem involves computing the slope and intercept of the regression line for data points (x, y) = [(1, 3.53), (2, 4.93), (3, 1.58), (4, 2.72), (5, 4.68), (6, 3.34)]. The linear regression line is y = -0.02x + 3.52.

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