1. Scatter Plots and Best-Fit Lines
Section 2.6
2.6: Scatter Plots and Best-Fit Lines
1/2/2019

2. Definitions Regression is the statistical study between variables
Scatterplot is a graph that helps understand the form, direction, and strength between two variables
Correlation is the strength and direction of the linear relationship between two variables
Correlation Coefficient is the measure of how well the data set is fit by through a model
R = –1 is where points lie near line with a negative slope
R = 0 is where points do not lie near any line
R = 1 is where points lie near line with a positive slope
2.6: Scatter Plots and Best-Fit Lines
1/2/2019

3. Types of Correlation
2.6: Scatter Plots and Best-Fit Lines
1/2/2019

4. Example 1
Tell whether the correlation coefficient for the data closest to –1, –0.5, 0, 0.5, or 1.
2.6: Scatter Plots and Best-Fit Lines
1/2/2019

5. Your Turn
Tell whether the correlation coefficient for the data closest to –1, –0.5, 0, 0.5, or 1.
2.6: Scatter Plots and Best-Fit Lines
1/2/2019

6. Steps of Curve Fitting Identify and list all of the data points
In the graphs, enter the data using STAT L1 should be the independent variable and L2 should be the dependent variable
STAT  CALC  select LinReg (ax + b) to get the equation
2.6: Scatter Plots and Best-Fit Lines
1/2/2019

7. Example 2
The table shows the U.S. daily oil production y (in thousands of barrels x years) after 1994.
Use the graphing calculator to find and graph the equation of the best-fitting line. (Round to the nearest thousandths)
What type of graph does this correlation represent?
Use the equation from part (a) to predict the daily oil production in 2012. x 1 2 3 4 5 6 7 8 y
6650
6560
6470
6450
6250
5880
5820
5800
5750
2.6: Scatter Plots and Best-Fit Lines
1/2/2019

8. Example 2
The table shows the U.S. daily oil production y (in thousands of barrels x years) after 1994.
Use the graphing calculator to find and graph the equation of the best-fitting line. (Round to the nearest thousandths) x 1 2 3 4 5 6 7 8 y
6650
6560
6470
6450
6250
5880
5820
5800
5750
2.6: Scatter Plots and Best-Fit Lines
1/2/2019

9. Example 2
The table shows the U.S. daily oil production y (in thousands of barrels x years) after 1994.
b) What type of graph does this correlation represent? x 1 2 3 4 5 6 7 8 y
6650
6560
6470
6450
6250
5880
5820
5800
5750
2.6: Scatter Plots and Best-Fit Lines
1/2/2019

10. Example 2
The table shows the U.S. daily oil production y (in thousands of barrels x years) after 1994.
c) Use the equation from part (a) to predict the daily oil production in 2012. x 1 2 3 4 5 6 7 8 y
6650
6560
6470
6450
6250
5880
5820
5800
5750
2.6: Scatter Plots and Best-Fit Lines
1/2/2019

11. Example 3
The table gives the systolic blood pressure y of patients x years old.
Use the graphing calculator to find and graph the equation of the best-fitting line. (Round to the nearest thousandths)
What type of graph does this correlation represent?
Use the equation from part (a) to predict the blood pressure when the patient is 72 years old. x 43 48 56 61 67 70 y
128
120
135
143
141
152
2.6: Scatter Plots and Best-Fit Lines
1/2/2019

12. Your Turn
The data below shows the population y (in millions) of Texas after 1997.
Use the graphing calculator to find and graph the equation of the best-fitting line. (Round to the nearest thousandths)
What type of graph does this correlation represent?
Use the equation from part (a) to predict the blood pressure when the patient in 2012.
What attributes can you conclude about the increase of population from 1997 to 2012? x 1 2 3 4 5 6 7 y
19.7
20.2
20.6
20.9
21.3
21.7
22.1
22.5
2.6: Scatter Plots and Best-Fit Lines
1/2/2019

13. Assignment
Page 117
3-19 odd, 25
There is no need to draw the scatterplot of the data
2.6: Scatter Plots and Best-Fit Lines
1/2/2019