Warm Up

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Friday, January 17 th. Warm Up. What is the end Behavior? What is the domain and range?. WARM UP – EOCT QUESTION 5. Scatter Plots. Topics to Cover. Correlation vs. Causation Calculating Correlation Line of best fit Least squared regression Residual plots. Regression.

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Warm Up

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Presentation Transcript

Friday, January 17th

Warm Up

What is the end Behavior?

What is the domain and range?

Scatter

Plots

Topics to Cover
• Correlation vs. Causation
• Calculating Correlation
• Line of best fit
• Least squared regression
• Residual plots

Regression

Correlation vs. Causation

Correlation

Causation

Means that one thing will cause the other.

A statistical way to measure the relationship between two sets of data.

Means that both things are observed at the same time.

You can have correlation without causation

There is a correlation (relationship) between the number of firemen fighting a fire and the size of the fire.

(The more firefighters at the scene means that there is a bigger fire.)

However, this doesn’t mean that bringing more firemen will cause the size of the fire to increase

Is it Causation or Correlation?

Ex 1. A recent study showed that college students were more likely to vote than their peers who were not in school.

Correlation

Ex 2. Mr. Suttlenoticed that there was more trash in the hallways after 2nd period than 1st period.

Correlation

Ex 3. You hit your little sister and she cries

Causation

Measuring Correlation
• Correlation is measured by the correlation coefficient, R.
• R is a number between -1 and 1.
• There are 4 traits to correlation:
• Form
• Direction
• Strength
• Outliers
1. FORM

Linear

No Correlation

Cubic

Exponential

2. Direction

Positive Correlation

Negative Correlation

POSITIVE

Positive correlations: as x increases, y increases or as x decreases, y decreases

• The more hours the athlete practices, the better he plays.
• The more efficiently a student studies, the higher his/her grades.

NegatIVE

Negative correlations: as x increases, y decreases or as x decreases, y increases

• The more miles driven, the less gas is left in the tank.
• The more often students wash their hands, the less likely they are to get sick!

NO CORRELATION

No correlation: there appears to be no trend

• Can you give me an example?!
3. Strength

Weak ---------------------------> Strong

R value (correlation coefficient)

0 ---------------------------> 1

Correlation Coefficient (r):
• number from -1 to 1 that measure how well a line fits a set of data pairs (x , y)
• If r is near -1, points lie close to a line with negative slope
• If r is near 1, points lie close to a line with positive slope
• If r is near 0, points don’t lie close to any line
• correlation of how 2 variables relate
• range from -1 to 1
• closer to 1 or -1 the stronger the correlation

Ex 1: 0.87, -0.81, 0.43, 0.07, -0.98

Ex 2: 0.32, -0.65, 0.63, -0.42, 0.04

0.07, 0.43, -0.81, 0.87, & -0.98

0.04, 0.32, -0.42, 0.63, & -0.65

Match the Correlation Coefficient to the graph

Graph

Correlation Coefficients

-1

-0.5

0

0.5

1

Match the Correlation Coefficient to the graph

Graph

Correlation Coefficients

-1

-0.5

0

0.5

1

Match the Correlation Coefficient to the graph

Graph

Correlation Coefficients

-1

-0.5

0

0.5

1

Match the Correlation Coefficient to the graph

Graph

Correlation Coefficients

-1

-0.5

0

0.5

1

Match the Correlation Coefficient to the graph

Graph

Correlation Coefficients

-1

-0.5

0

0.5

1

Outliers

Data that doesn’t fit in

Positive, Negative, or No Correlation?

• The number of hours you work vs. The amount of money in your bank account

Positive

B. The number of hours workers receive safety training vs. The number of accidents on the job.

Negative

C. The number of students at Hillgrovevs. The number of dogs in Atlanta

No Correlation

Positive, Negative, or No Correlation?

D. The number of heaters sold vs. The months in order from February to July

Negative

E. The number of rice dishes eaten vs. The number of cars on I-75 throughout the day

No Correlation

F. The number of calories burned/lost vs. The amount of hours walked

Positive