Coordinate Algebra Linear Regression Day 1 Notes Date: _____ COMPLETED Scatter plots : show the relationship between two variables
Correlation : the degree to which two variables are associated
The graph below shows the relationship between height and age.
Height
Age
Although it isn’t linear, there is clearly a ____POSITIVE______correlation between age and height. This means that as age increases, height increases.
The graph below shows the relationship between price of an object and the number purchased by customers.
# Purchased
Price
This illustrates a ______NEGATIVE___ correlation. This means as price of an object increases, the number purchased decreases. In other words, if the price of an object goes up, fewer people will buy that object.
The graph below shows the relationship between number of points scored on a test and height.
Points Scored
Height
There is no correlation between height and points scored because there is no definable pattern. Therefore, height and number of points scored on a test have no relationship. The correlation coefficient, denoted by the letter r, is a number from -1 to 1 that measures the strength and direction of the correlation between two variables.
r r r (no correlation) (strong negative) (strong positive)
-1 0 1
When r is near 1: the points on a scatter plot lie close to a line with a positive slope there is a strong __positive___ correlation between the points
When r is near -1: the points on a scatter plot lie close to a line with a negative slope there is a strong __negative___ correlation between the points
When r is near 0: the points on a scatter plot do not lie close to any line plots are said to have __no____correlation
What would you say about the correlation of this plot? Negative Correlation
A line of best fit is a straight line that best represents the data on a scatter plot.
The equation of the best fit line is y = ax + b .
In this form, a is the slope of your best fit line and b is the y-intercept .
Ex1) Find an equation for the line of best for the plot to the right. The data and line are already drawn.
1. Pick two points on the line and find the slope between them.
Slope: (-4, 2) & (5, 5) Try to pick ordered pairs at the extremes of the = = =
2. Using y = ax + b , solve to find b. Pick one of the 2 = −4 + b ordered pairs to 2 = − + b use with the b = 3.33
3. Write out your line of best fit.
y = x + 3.33
Ex2) Find the line of best fit for the relationship between the total fat and total calories for various sandwiches. Use the graph to the right.
1. Pick two points on the line and find the slope between them.
Slope: (0, 200) & (34, 585)