2. Analyzing Data using the Graphing Calculators Correlation & Slope Notes 3.2

3. Introduction A man was in a hot-air balloon. Soon he found himself lost with nothing but green fields for as far as the eye could see. Eventually, he floated over a man who was walking his dog. He leaned over the basket and yelled out, “Hello! Where am I?”

4. Introduction The man on the ground replied, “You’re about 20 feet above the ground in a hot-air balloon.” The balloonist angrily shouted back, “You must be a statistician.” “Why do you say that?” asked the man on the ground. “Well,” came the reply, “You’re absolutely correct but your answer is completely useless.”

5. Introduction “Oh, I see,” replied the walker, “And you must be a manager.” “Actually, you’re right,” said the balloonist. “How did you know?” “First, you were lost. Then, after deciding what information you needed to solve the problem, you asked someone else to get it for you. Now that you have the information, you’re still lost, but it’s someone else’s fault.”

6. Asking the right question- Building a Hypothesis Many times scientists will collect and graph data from the same subjects to see if there is a relationship between them.

7. Asking the right question- Building a Hypothesis: Examples Is a person’s height related to their shoe size? Does studying more hours mean getting a higher grade? Does increasing the pressure of a room decrease the volume of a balloon?

8. Collecting the Data Data is written on a table as coordinate pairs (x,y) X is the input or independent variable Y is the output or dependent variable

9. 1) Analyzing Data - Direction of the relationship Data can have: Positive relationship Negative relationship No relationship

10. Result #1 positive relationship. As x increases, y also increases.

11. Result #2: negative relationship. As x increases, y decreases.

12. Result #3: No relationship. As x increases, no trend in y

13. 2) Analyzing Data - Strength of Relationships Correlation (r) measures the strength of the relationship If all of the data falls perfectly on a line, it is considered perfect.

14. A perfect correlation has a value of one (1)...

15. …or a value of negative one (-1)

16. Strength of correlation (r) can vary r = +.80 r = +.60 r = +.40 r = +.20

17. Strong Correlation Exam score Quality of Breakfast r = + 0.8 Best Fit line

18. Medium Correlation Weight Shoe Size r = + 0.4 Best Fit line

19. Weak Correlation Weight Shoe Size r = - 0.2 Best Fit line

20. Slope (a) - A measurement of change Increasing slope

21. Slope (a) - A measurement of change Increasing slope

22. Slope (a) - A measurement of change Increasing slope

23. a Measuring slope (a) Lines are written in the form y=ax+b. Which means that the number before the x would be the slope.

24. Plotting lines on the TI-83 - Preparation 1. Press [Y=] and [CLEAR] any previous data 2. Reset [ZOOM] to [6:Zstandard]

25. Plotting lines on the TI-83 - Analyzing the slope 1. Press [Y=] and type the equation: Y 1 =.5x+0 2. Press [GRAPH] 3. Press [Y=] and add the equation Y 2 = 1x+0 4. Press [Y=] and add the equation Y 3 =2x+0 5 Press [Y=] and add the equation Y 4 =3x +0

26. Plotting lines on the TI-83 - What happens to the slope of the line? Predict what the equation Y=4x+0 would look like. Predict what the equation Y=-4+0 would look like. Check your predictions.

27. The Y-intercept In the form Y=ax+b, the number that represents “b” is where the line crosses the Y axis. b

28. Plotting lines on the TI-83 - Preparation 1. Press [Y=] and [CLEAR] all your equations

29. Plotting lines on the TI-83 - Analyzing the Y-intercept 1. Type the equation: Y 1 = 1x+0 2. Press [GRAPH] 3. Type the equation: Y 2 =1x+1 4. Type the equation: Y 3 =1x+2 5. Type the equation: Y 4 =1x+3 6. Type the equation: Y 5 =1x+4

30. Plotting lines on the TI-83 - Analyzing the Y-intercept What would the equation Y 5 =1x-1 look like on a graph? Check your prediction.

31. Plotting lines on the TI-83 - Analyzing the Y-intercept What would the equation Y 5 =1x-1 look like on a graph? Check your prediction. What is the slope of this line?

32. Making Predictions 1.One of the main purposes for graphing data is for making predictions. 2.For a given value of x, we can predict a future value of y

33. Review What would a positive relationship between data look like on a graph? What would a negative relationship between data look like on a graph? What would no relationship between data look like on a graph?

34. Review What does a perfect correlation look like? What number represents a perfect correlation? What symbol represents correlation? What does a correlation of 0 look like on a graph?

35. Review What is the symbol for slope? What is the equation format for a line? What does the symbol b represent? What does b tell us about the graph?