Question 2
Check 0/5 ptsRetries 3
x	1	2	3	4	5	6
y	703	826	1094	1338	1602	2189


Use linear regression to find the equation for the linear function that best fits this data. Round to two decimal places.

y
  = 


To find the linear function that best fits the given data points using linear regression, we need to determine the slope \( m \) and the y-intercept \( b \) in the equation:

\[
y = mx + b
\]

The data points given are:

\[
x = [1, 2, 3, 4, 5, 6]
\]
\[
y = [703, 826, 1094, 1338, 1602, 2189]
\]

We can use the formulas for slope \( m \) and intercept \( b \):

\[
m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}
\]
\[
b = \frac{(\sum y) - m(\sum x)}{n}
\]

Where:
- \( n \) is the number of data points (in this case, 6),
- \( \sum x \) is the sum of all \( x \) values,
- \( \sum y \) is the sum of all \( y \) values,
- \( \sum xy \) is the sum of the product of corresponding \( x \) and \( y \) values,
- \( \sum x^2 \) is the sum of the squares of the \( x \) values.

Let's calculate these values and determine the equation of the best-fit line. I'll work through the computations next.The equation for the linear function that best fits the given data is:

\[
y = 285.77x + 291.80
\]

Let me know if you'd like a more detailed explanation, or if you have any further questions!

Here are 5 related questions you might consider:
1. How is the slope of a line interpreted in a linear regression context?
2. What role does the y-intercept play in the linear regression equation?
3. Can you calculate the predicted \( y \) values for \( x = 7 \) using the equation?
4. How would the equation change if there were an outlier in the data set?
5. How is the goodness-of-fit of this linear regression model typically measured?

**Tip:** In linear regression, the slope indicates how much \( y \) changes for each unit increase in \( x \).

Use linear regression to find the equation for the linear function that best fits this data. Round to two decimal places.

x = [1, 2, 3, 4, 5, 6]

y = [703, 826, 1094, 1338, 1602, 2189]

Use linear regression to find the best-fit line for the data points x = [1, 2, 3, 4, 5, 6] and y = [703, 826, 1094, 1338, 1602, 2189]. Learn step-by-step how to calculate the slope and intercept using key formulas. Suitable for students in Grades 9-12.

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