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Part 1
For the data given​ below, answer parts ​(a) through ​(f).
x
1
2
3
4
5
6
7
y
4
6
7
10
12
14
16
Graph the line found in
y= 2x + 2 on the scatter plot.     Use a graphing utility to find the line of best fit.

The graph above shows the scatter plot of the given data points, the line \( y = 2x + 2 \) (in green), and the line of best fit (in red dashed).

### Line of Best Fit:
The equation for the line of best fit is:
\[
y = 2.04x + 1.71
\]
This line was calculated using the least squares method to best fit the given data points.

Do you have any questions, or would you like further details on the steps involved? 

Here are 5 related questions to explore further:
1. How is the slope of a line calculated in linear regression?
2. What is the significance of the \( r \)-value in linear regression?
3. How do we interpret the y-intercept in a linear equation?
4. Can the line \( y = 2x + 2 \) be considered a good fit for the data?
5. What is the standard error in the context of the regression line?

**Tip**: The line of best fit helps predict values of \( y \) for given \( x \)-values by minimizing the squared distances between observed points and the line.

For the data given​ below, answer parts ​(a) through ​(f).
x: 1, 2, 3, 4, 5, 6, 7
y: 4, 6, 7, 10, 12, 14, 16
Graph the line found in y = 2x + 2 on the scatter plot. Use a graphing utility to find the line of best fit.

Analyze the data set (x: 1, 2, 3, 4, 5, 6, 7 and y: 4, 6, 7, 10, 12, 14, 16) to graph the line y = 2x + 2 and use a graphing utility to find the line of best fit. This exercise demonstrates how to calculate and interpret the line of best fit using linear regression. Suitable for Grades 9-12 students learning about scatter plots and data analysis.

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