1. Dr. Fowler  AFM  Unit 8-5 Linear Correlation
Be able to construct a scatterplot to show the relationship between two variables.
Understand the properties of the linear correlation coefficient.
Use linear regression to find the line of best fit for a set of data points.

2. Scatterplots
To determine whether there is a correlation between two variables, we obtain pairs of data, called data points, relating the first variable to the second.
To understand such data, we plot data points in a graph called a scatterplot.

3. Scatterplots
Example: An instructor wants to know whether there is a correlation between the number of times students attended tutoring sessions during the semester and their grades on a 50-point examination. The table shows the data for 10 students. Represent these data points by a scatterplot and interpret the graph.
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4. Scatterplots
Solution: We plot the points (18, 42), (6, 31), (16, 46), and so on.
As the number of tutoring sessions increases, the grades also generally increase.

5. Linear Correlation

6. Linear Correlation
There is a positive correlation between the variables x and y if whenever x increases or decreases, then y changes in the same way. We will say that there is a negative correlation between the variables x and y if whenever x increases or decreases, then y changes in the opposite way.

7. Linear Correlation 1. Compute r for n pairs of data.
2. If the absolute value of r exceeds the number in the column labeled α = .05 on line n, then there is less than a .05 (5%) chance that the variables do not have significant linear correlation.
3. If the absolute value of r exceeds the number in the column labeled α = .01 on line n, then there is less than a .01 (1%) chance that the variables do not have significant linear correlation.

8. Linear Correlation
Linear correlation exists between two variables if, when graphed, the points in the graph tend to lie in a straight line. The linear correlation coefficient allows us to compute to what degree the points of a scatterplot lie along a straight line.

9. EX: Calculate the Linear Correlation Coefficient: (2,11),(2,6),(10,6),(18,2)

10. The Line of Best Fit
We wish to find the line that best models our data.
This line is called the line of best fit. It is the line that minimizes the sum of all the vertical distances from the data points to the line.

11. The Line of Best Fit
EX: Find the line of best fit for: (24,15),(26,13),(28,20),(30,16),(32,24)
M = 5⦁2506 −(140)(88) −(19,600)
B= 88 −(1.05)⦁(140) 5
B= −59 5
=− 11.8
M =
=1.05
y =1.05x −11.8

12. The Line of Best Fit

13. y-intercept: Slope: The line of best fit is
Example: Find the line of best fit for the set of data points below:
Slope:
y-intercept:
The line of best fit is

14. Excellent Job !!! Well Done