Sections 3.1 - 3.3

1. Sections 3.1 - 3.3 Review

2. Relationship between two variables • Bivariate data

3. What three shapes are possible for a bivariate data relationship?

4. What three shapes are possible for a bivariate data relationship? • Linear • Curved • No shape

5. Shape : Linear

6. Shape : Linear

7. Shape: Curved

8. Shape: Curved

9. Shape: Curved

10. Shape: None

11. Shape: None

12. The line on the plot is the ____________.

13. The line on the plot is the least squares regression line, LSRL, or regression line.

14. Two main reasons to fit a line to a set of data:

15. Two main reasons to fit a line to a set of data: 1) to find a summary or model that describes relationship between two variables 2) to use the line to predict value of y when you know value of x

16. To make a reasonable prediction, what needs to be true about: A) shape of data? B) strength of relationship?

17. To make a reasonable prediction, what needs to be true about: A) shape of data? linear B) strength of relationship?

18. To make a reasonable prediction, what needs to be true about: A) shape of data? linear B) strength of relationship? Stronger the better

19. Usually, the independent variable, x, is on the horizontal axis. Dependent variable, y, is on vertical axis,

20. Statistics, not Algebra! The variable on the x-axis is called the __________ or __________ variable. The variable on the y-axis is called the __________ or __________ variable.

21. Statistics, not Algebra! The variable on the x-axis is called the predictor or explanatoryvariable. The variable on the y-axis is called the __________ or __________ variable.

22. Statistics, not Algebra! The variable on the x-axis is called the predictor or explanatory variable. The variable on the y-axis is called the predicted or response variable.

23. Which is correct? Year vs Minimum Wage or Minimum Wage vs Year?

24. Which is correct? Year vs Minimum Wage or Minimum Wage vs Year?

25. Two types of predictions:

26. Two types of predictions: 1) interpolation – making prediction when value of x falls within range of the data

27. Two types of predictions: 1) interpolation – making prediction when value of x falls within range of the data 2) extrapolation – making prediction when value of x falls outside range of actual data

28. Two types of predictions: 1) interpolation – making prediction when value of x falls within range of the data 2) extrapolation – making prediction when value of x falls outside range of actual data Interpolation fairly safe Extrapolation risky especially the further x-value is outside range of actual data

29. Prediction error: difference between the actual value of y and value of y predicted from a regression line Usually unknown except for the points used to construct the regression line, whose prediction errors are called residuals

30. Residual = observed value of y – predicted value of y Residual = y - y

31. Residual is the signed vertical distance from an observed data point to the regression line. Positive if point above the line Negative if point below the line 0 if point on the line

32. Least squares regression line, also called least squares line or regression line, is the line for which the sum of the squared errors or SSE is as small as possible. SSE = (residuals)2

33. Find the least squares line for this passenger jets data.

34. Put explanatory values in L1 and response values in L2

35. Put explanatory values in L1 and response values in L2 STAT CALC 8. LinReg (a + bx) LinReg (a + bx) L1, L2, Y1 (Y1 needed if want to show LSRL on graph)

36. Put explanatory values in L1 and response values in L2 STAT CALC 8. LinReg (a + bx) LinReg (a + bx) L1, L2, Y1 To get Y1, go to VARS, Y-VARS, 1: Function, ENTER, 1: Y1, ENTER

37. LinReg y = a + bx a = 366.6666667 b = 16 r2 = .9795918367 r = .9897433186 So, what is equation for LSRL?

38. LinReg y = a + bx a = 366.6666667 b = 16 r2 = .9795918367 (Turn Diagnostic On) r = .9897433186 So, what is equation for LSRL?

39. LinReg y = a + bx a = 366.6666667 b = 16 r2 = .9795918367 r = .9897433186 So, what is equation for LSRL? y = 367 + 16x Is this it?

40. LinReg y = a + bx a = 366.6666667 b = 16 r2 = .9795918367 r = .9897433186 So, what is equation for LSRL? y = 367 + 16x Is this it? No! Need equation in context!

41. So, what is equation for LSRL? y = 367 + 16x Is this it? No! Need equation in context! Cost = 367 + 16(seats)

42. Cost = 367 + 16(seats) Interpret the slope and y-intercept.

43. Cost = 367 + 16(seats) Interpret the slope and y-intercept. Slope: For each additional seat, the cost increases by about $16 per hour

44. Cost = 367 + 16(seats) Interpret the slope and y-intercept. Slope: For each additional seat, the cost increases by about $16 per hour y-intercept: If a passenger jet had 0 seats, it would cost $367 per hour to operate.

45. Correlation What do you recall about correlation?

46. Correlation • Measures strength and direction of a linear relationship between two variables • Numerical value between -1 and 1, inclusive • How tightly packed points of scatterplot are about the LSRL • Correlation and slope always have the same sign

47. Sketch ellipse around points in scatterplot. If ellipse has points scattered throughout and points appear to follow a linear trend, then correlation is a reasonable measure of strength of the relationship.

48. No shape

49. Does a higher correlation mean the relationship is more like a line, less like a line, or neither?

50. Does a higher correlation mean the relationship is more like a line, less like a line, or neither? Neither if misused