Statistical Reasoningfor everyday life

Intro to Probability and Statistics

Mr. Spering – Room 113

7.1 Correlation? Correlation…

Correlation exists between two variables when higher values of one variable consistently go with higher values of another or when higher values of one variable consistently go with lower values of another.

Examples: Height and weight Demand and price Practice time and skill Smoking and lung cancer High cholesterol and heart disease Etcetera, etcetera, etc.

7.1 Correlation?Scatter Plots…Scatter Plot is a graph in which each point corresponds to the values of two variables……To be more specific, a scatter plot, scatter diagram or scatter

graph is a chart that uses Cartesian coordinates to display values for two variables. The data is displayed as a collection of points, each having one coordinate on the horizontal axis and one on the vertical axis. A scatter plot does not specify dependent or independent variables. Either type of variable can be plotted on either axis. Scatter plots represent the association (not causation) between two variables.

7.1 Correlation?•Positive Correlation…

Both variables tend to increase (or decrease) together.

7.1 Correlation?•Negative Correlation…

Two variables tend to change in opposite directions, with one increasing while the other decreases.

7.1 Correlation?•No Correlation…

There is no apparent relationship between the two variables.

Example:

Height and eye color

7.1 Correlation?•Nonlinear relationship…

The two variables are related, but the relationship results in a scatter plot that does not follow a straight-line pattern.

7.1 Correlation?•Correlation Coefficient…

Coefficient represented by the letter, r, measures the strength of a correlation.

[TI-84 plus → STAT; TESTS; LinRegTTest… and LinRegTInt…scroll down, look for r-value]

INTERPOLATING???

7.1 Correlation?• Properties of the Correlation Coefficient, r.

1. The value of r is always between -1 and 1. That is -1 ≤ r ≤ 1.

2. A positive correlation has a positive correlation if a scatter diagram’s points lie closer to a rising straight line. They will have an r-value closer to 1. A perfect positive correlation has a coefficient of 1.

3. A negative correlation has a negative correlation if a scatter diagram’s points lie closer to a descending straight line. They will have an r-value closer to -1. A perfect negative correlation has a coefficient of -1.

4. If there is no correlation, the points do not follow any ascending or descending straight lines, and the r value is close to 0.

7.1 Correlation?• Properties of the Correlation Coefficient, r.

LETS PLAY?!?!?!?!?!? http://argyll.epsb.ca/jreed/math9/strand4/scatterPlot.htm

7.1 Correlation?• Properties of the Correlation Coefficient, r.

• Calculating the correlation coefficient…

2 2 2 2

( ) ( ) ( )

( ) ( ) ( ) ( )

n xy x yr

n x x n y y

Don’t get confused or mad, there are no secrets in mathematics!

7.1 Correlation?

HOMEWORK: pg 295 # 1-17 all, # 23