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 $y$.