1. Scatterplots and Correlation

2. Scatter Plots and Correlation
Scatter plots =discrete graph which shows relationships between two sets of data.
Correlation = describes the type of relationship represented
Strong Correlation = if the points (dots) are close to the line
Weak Correlation = if the points are further from the line (spread out)
Positive Correlation / “Trend”= both data sets increase together (an increasing graph)
Negative Correlation / “Trend”= as one data set increases, the other decreases (a decreasing graph)
Positive Correlation
No correlation
Negative Correlation

3. Patterns in scatter plots
Scatter Plots show Linear Associations when the points cluster along a straight line.
Linear Association
Linear Association

4. Patterns in scatter plots
Scatter Plots show Non-Linear Associations when the points do not cluster along a straight line
Non- Linear Association
Non- Linear Association

5. Patterns in scatter plots
Outliers are values much greater or much less than the others in a data set. They lay outside the cluster of correlation
Scatter plots do not always contain outliers.
Do you notice any outliers in these scatter plots?

6. Linear Associations
Line of Best Fit = is the line that best approximates the linear relationship between two data sets (comes closest to all of the dots on the graph)
Linear Regression Equation = the equation that describes the line of best fit
Linear Regression = models the relationship between two variables in a data set by producing a line of best fit

7. Placing a Line of Best Fit
Select which line is the correct Line of Best Fit / Linear Regression A. A. A. A. B. B. B. B.

8. Correlation Coefficient
Correlation Coefficient= indicates how closely data points are to forming a straight line (shows the strength of correlation).
“r” represents the correlation coefficient
Only for scatter plots that appears to have a linear association
The value of the correlation coefficient is -1 ≤ r ≤ 1
+1 is perfect positive correlation, very strong (an actual line)
0 is no correlation
-1 is perfect negative correlation, very strong (an actual line with negative slope).

9. Perfect straight decreasing line
Perfect straight increasing line

10. Estimate r value (correlation coefficient)
Speed of Car & Fuel Efficiency
Cost of Property & Number of Spaces from GO on Monopoly Game Board
The correlation coefficient is
r = 0.9
This means that there is a STRONG Positive Correlation.
The correlation coefficient is
r = 0.7
This means that there is a MODERATE Positive Correlation.

11. Estimate r value (correlation coefficient)
Price of a Used Car and Number of Miles on the Odometer
Amount of Gas to Heat a House and Average Monthly Outdoor Temperature
The correlation coefficient is
r = -0.6
This means that there is a MODERATE Negative Correlation.
The correlation coefficient is
r = -0.8
This means that there is a STRONG Negative Correlation.

12. Estimate r value (correlation coefficient)
Duration of a Rollercoaster Ride & the Height of the First Drop
GPA & Weight of Student
The correlation coefficient is
r = 0.3
This means that there is a WEAK Positive Correlation.
The correlation coefficient is
r = 0
This means that there is a NO Correlation.

13. Paycheck & Hours Worked
Estimate r value (correlation coefficient)
Paycheck & Hours Worked
If you had a job and made $8.25 per hour, the graph at the right would show the amount of your paycheck after working x number of hours.
In this example, r = 1 because the hours you work and the amount of money you earn, show PERFECT Positive Correlation.
The slope is 8.25 not 1.
The r value and the slope are two different things.
The correlation coefficient will have the SAME sign as the slope but rarely the same value.