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Warm Up

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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  1. Friday, January 17th Warm Up What is the end Behavior? What is the domain and range?

  2. WARM UP – EOCT QUESTION 5

  3. Scatter Plots

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

  5. Regression Correlation vs. Causation

  6. 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.

  7. 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

  8. 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

  9. 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

  10. 1. FORM Linear Quadratic No Correlation Cubic  Exponential         

  11. 2. Direction Positive Correlation Negative Correlation

  12. 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.

  13. 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!

  14. NO CORRELATION No correlation: there appears to be no trend • Can you give me an example?!

  15. 3. Strength Weak ---------------------------> Strong R value (correlation coefficient) 0 ---------------------------> 1

  16. 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

  17. Put the correlation coefficients in order from weakest to strongest 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

  18. Try this: Calculate R

  19. Match the Correlation Coefficient to the graph Graph Correlation Coefficients -1 -0.5 0 0.5 1

  20. Match the Correlation Coefficient to the graph Graph Correlation Coefficients -1 -0.5 0 0.5 1

  21. Match the Correlation Coefficient to the graph Graph Correlation Coefficients -1 -0.5 0 0.5 1

  22. Match the Correlation Coefficient to the graph Graph Correlation Coefficients -1 -0.5 0 0.5 1

  23. Match the Correlation Coefficient to the graph Graph Correlation Coefficients -1 -0.5 0 0.5 1

  24. Outliers Data that doesn’t fit in

  25. 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

  26. 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

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