1. Welcome to .
Week 12 Thurs .
MAT135 Statistics

2. In-Class Project Radiation Experiment

3. Correlation
A relationship can be seen by graphing the independent and dependent variables in a scatter graph

4. Correlation
A linear relationship is very common

5. Correlation
When we calculated a correlation coefficient, we said it was a measure of the closeness to a linear relationship between the two variables

6. Line of Best Fit
That means, we could find the formula for a line that would be the best fit for the two variables

7. Line of Best Fit
We “fit” a line to the data

8. Line of Best Fit
Real-world data rarely lands exactly on a straight line

9. Line of Best Fit
But we fit the “best” line to the data

10. Line of Best Fit
When you graph two variables on an x-y plot, you can fit a line through the data called a “trend line”

11. Line of Best Fit
This trend line is a “line of best fit” to the data

12. Line of Best Fit
The “line of best fit” is created by minimizing the total vertical distance of all the points to the line (deviations)

13. Regression
This line of best fit is called the “regression” line

14. Regression
Because it is a line, it has an equation: y = b + mx m = slope b = y-intercept

15. Regression
NOTE: The slope “m” and the correlation coefficient “r” will both have the same sign

16. Regression
R2 tells how closely the regression line “fits” the data – “goodness of fit”

17. Regression
As you can imagine, the calculations for correlation and the regression line are scary

18. Regression
Hooray for the TI83/4 and Excel!

19. Regression
Francis Galton

21. Questions?

22. Regression
To do a regression analysis on your TI83/4, you use the same procedure as we used to calculate the correlation coefficient

23. Regression
Efficiency of a lever

24. Regression Efficiency of a lever distance in inches, weight in grams

25. Efficiency of a lever Clear your memory Enter your data
Regression
PROJECT QUESTION
Efficiency of a lever
distance in inches, weight in grams
Clear your memory
Enter your data
Distance
Weight
104 1
175 2
245 3
336 4
429 5
514 6
608 7
695

26. Efficiency of a lever Clear your memory Enter your data STAT CALC
Regression
PROJECT QUESTION
Efficiency of a lever
distance in inches, weight in grams
Clear your memory
Enter your data
STAT
CALC
LinReg
ENTER
Distance
Weight
104 1
175 2
245 3
336 4
429 5
514 6
608 7
695

27. Regression
PROJECT QUESTION
Efficiency of a lever LinReg y=ax+b a= b= r2= r=

28. Regression
PROJECT QUESTION
Efficiency of a lever LinReg y=ax+b a= b= r2= r= Is this a strong relationship?

29. Regression
One of the prime features of regression is that the equation can be used to give estimates

30. Regression
PROJECT QUESTION
LinReg y=ax+b a= b= r2= r= What weight would you estimate for a distance of 2.5 inches?

31. Regression
PROJECT QUESTION
LinReg y=ax+b a= b= r2= r= What weight would you estimate for a distance of 2.5 inches? y = 85.7× = 302.5g

32. Questions?

33. Time Series
A lot of things happen over time Time is called the “independent” variable – we can’t control it! The variable that changes over time we call the “dependent” variable

34. Time Series
Data that change over time are called “time series” data

35. Time Series
A regression analysis for time series data is called a “time series” analysis

36. Time Series
One of the prime features of a time series analysis is that the equation can be used to give forecasts

37. Time Series
One of the prime features of a time series analysis is that the equation can be used to give forecasts … bosses LIKE forecasts!

38. Time Series Our radiation experiment is a time series Time Temp Silver
Temp Black
192 10
180
178 20
169
162 30
160
152 40
143 50
144
134 60
138
128

39. (Previous class data) Clear your memory Enter the data LinReg L1,L2
Time Series
PROJECT QUESTION
(Previous class data) Clear your memory Enter the data LinReg L1,L2
Time
Temp Silver
Temp Black
192 10
180
178 20
169
162 30
160
152 40
143 50
144
134 60
138
128

40. Time Series
PROJECT QUESTION
LinReg y=ax+b a= b= r2= r=
Time
Temp Silver
Temp Black
192 10
180
178 20
169
162 30
160
152 40
143 50
144
134 60
138
128

41. Time Series
PROJECT QUESTION
LinReg y=ax+b a= b= r2= r= Is this a strong relationship?

42. Time Series
PROJECT QUESTION
LinReg y=ax+b a= b= r2= r= What does “r” tell you that RSQ does not?

43. Time Series
PROJECT QUESTION
LinReg y=ax+b a= b= r2= r= What would your forecast be for 70 minutes?

44. Time Series
PROJECT QUESTION
But that’s just the silver container! DO NOT CLEAR YOUR MEMORY STAT CALC LinReg L1,L3

45. Time Series
PROJECT QUESTION
LinReg L1,L3 y=ax+b a= b= r2= r=

46. Time Series
PROJECT QUESTION
LinReg L1,L2 LinReg L1,L3 y=ax+b y=ax+b a= a= b= b= r2= r2= r= r= Which is going down faster?

47. Time Series
PROJECT QUESTION
Silver can: temp = -.9×(time) Black can: temp = -1.1(time)

48. Time Series
PROJECT QUESTION
The graph:

49. Time Series
PROJECT QUESTION
Are the lines good fits?

50. Time Series
PROJECT QUESTION
Are the forecasts good?

51. Time Series
Even though a time series may have a VERY high correlation, this does not guarantee an accurate forecast

52. Time Series
Many time series are not really linear (even though they may look like it for awhile)

53. Questions?

54. You survived! Turn in your homework! Don’t forget your homework
due next week!
Have a great
rest of the week!