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
=
m
x
+
b
x	1	2	3	4	5	6
y	77	96	125	141	156	192
Linear Regression Equation:    

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.

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 the form of an equation y = mx + b x 1 2 3 4 5 6 y 77 96 125 141 156 192

Learn how to use linear regression to find the equation of the line that best fits the data set (x = [1, 2, 3, 4, 5, 6], y = [77, 96, 125, 141, 156, 192]). This problem involves calculating the slope and y-intercept using statistical formulas, suitable for students in Grades 10-12.

Math Problem Statement

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

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