1. 2-5 Using Linear Models
Make predictions by writing linear equations that model real-world data.

2. Scatter Plots
A scatter plot is a graph that displays two sets of data as ordered pairs.
Scatter plots can help show whether or not two sets of data are related.

3. Making a Scatter Plot Make a scatter plot for the data
What’s a car worth?
Age (yr)
Value (dollars) 3
11,000 1
15,000 2
12,000 4
8,000 7
3,000 5
7,000 8
1,000
6,000
10,000 6

4. Correlation A correlation is a relationship between the sets of data
Also called a trend
Positive correlation or trend

5. Correlation
Negative correlation or trend

6. Correlation
No correlation or trend

7. Line of Best Fit
A line you draw on a graph to approximate the relationship between data sets.
Also called a trend line
A line of best fit should have an equal number of data points on each side
If there is no correlation, you cannot draw a line of best fit

8. You Try! Create a scatter plot for the data and draw the trend line. 25 4 3
3.5 7
4.5 9 6

9. Making Predictions What is the approximate weight of a
7 month old panda?
We have just used interpolation to
estimate a value between two known values using a line of best fit.
Extrapolation is used to predict a value outside the range of known values.
Ex: Use your model to find the body weight of a 3-year old panda.

10. Causation
A change in one quantity causes a change in the second quantity.
Correlation does not always imply causation

11. Using a Calculator
Correlation coefficient (r) can be found using a graphing calculator.
Ranges between -1 and 1
The nearer r is to 1 or -1, the more closely the trend line fits the data
r close to 1 shows a strong positive correlation
r close to -1 shows a strong negative correlation
r close to 0 means a weaker correlation or no correlation

12. Using a Calculator Press STAT and then 1 to select EDIT
Enter x-values into L1 and y-values into L2
(if x-values are years, do not enter the year, but enter 1 for one year from the start, 2 for 2 years from start, etc.)
Press STAT then move Right to the CALC menu
Move Down to LinReg(ax+b) and press Enter
Press Enter again
a will represent slope
b will represent the y-intercept
And r will show the correlation coefficient (NOT r2)

13. Assignment
ODDS
P.96 #7-17