
Given the table of values.

Table of Values
x	-2	1	6	-1	3	4	8	-4
y	1	4	8	2	5	6	9	0
Determine the line of best fit.

Group of answer choices

y = 0.5x + 2.9

y = 0.8x + 2.7

y = 2.7x + 0.8

y = 2.9x + 0.8

To determine the line of best fit, we need to apply the **least squares method**, which calculates the slope and y-intercept of the line that best fits the given data points. We are looking for an equation in the form:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept.

Let's go through the necessary steps to find the equation of the line of best fit.

### 1. Mean of x and y:
We begin by calculating the mean of the \(x\) values and the mean of the \(y\) values.

### 2. Calculate slope (m):
The slope \(m\) is given by the formula:

\[
m = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}
\]

### 3. Calculate intercept (b):
The intercept \(b\) is given by the formula:

\[
b = \bar{y} - m\bar{x}
\]

I'll calculate the slope and intercept to get the line of best fit.The equation of the line of best fit is:

\[
y = 0.79x + 2.90
\]

This corresponds most closely to the option:

\[
y = 0.8x + 2.7
\]

Would you like further details on the calculations or steps? Here are five related questions:

1. How is the least squares method used to find the best fit line?
2. What is the significance of the slope and y-intercept in this context?
3. How can you calculate the correlation coefficient for this data set?
4. What are some limitations of using linear regression for non-linear data?
5. How do you determine if a linear model is appropriate for the given data?

**Tip:** When calculating the line of best fit, rounding is important to match the answer choices.

Given the table of values: x = [-2, 1, 6, -1, 3, 4, 8, -4] and y = [1, 4, 8, 2, 5, 6, 9, 0], determine the line of best fit. Group of answer choices: y = 0.5x + 2.9, y = 0.8x + 2.7, y = 2.7x + 0.8, y = 2.9x + 0.8.

Determine the line of best fit using the least squares method for the given data points: x = [-2, 1, 6, -1, 3, 4, 8, -4] and y = [1, 4, 8, 2, 5, 6, 9, 0]. This tutorial explains key mathematical concepts such as linear regression, slope, and intercept, suitable for Grades 10-12.

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