Use linear regression to find the equation for the linear function that best fits this data. Round both numbers to two decimal places. Write your final answer in a form of an equation y

To find the equation of the linear function that best fits the given data, we will use the formula for linear regression:

$y = mx + b$

where:

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

Given dataTo find the equation of the linear function that best fits the given data, we will use the formula for linear regression:

$y = mx + b$

where:

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

Given

$x = [1, 2, 3, 4, 5, 6]$ $y = [77, 96, 125, 141, 156, 192]$

To compute $m$ and $b$, we use the following formulas:

1. Slope (m): $m = \frac{n \sum xy - \sum x \sum y}{n \sum x^2 - (\sum x)^2}$

2. Intercept (b): $b = \frac{\sum y - m \sum x}{n}$

Where $n$ is the number of data points. Let’s calculate the values of $m$ and $b$.The equation of the linear function that best fits the given data is:

$y = 22.03x + 54.07$

Do you have any questions or would you like further details?

Here are 5 related questions to explore further:

1. How is the slope $m$ in a linear regression interpreted?
2. What role does the y-intercept $b$ play in a linear equation?
3. How can we assess the accuracy of a linear regression model?
4. What is the difference between linear regression and polynomial regression?
5. How does increasing the number of data points affect the linear regression line?

Tip: When plotting data, you can visually assess how well the linear regression line fits the data by checking how close the points are to the line.