1. Section 3.4
Day 2

2. When is it appropriate to use a least squares regression line (LSRL) or correlation?

3. Only when you have a linear pattern.
When is it appropriate to use a least squares regression line (LSRL) or correlation?
Only when you have a linear pattern.

4. Linear Pattern or Not?

5. Linear Pattern or Not? No… YES …
…if “outlier” is excluded, then a circle would be used = NO SHAPE.
YES …
…if “outlier” is included, an ellipse could be formed then LINE could be used.

6. Linear Pattern or Not?

7. Linear Pattern or Not?
Yes
(no pattern to residuals)

8. Linear Pattern or Not?

9. Linear Pattern or Not? No
(Curved data)

10. Linear Pattern or Not?

11. Linear Pattern or Not?
Yes
(no pattern to residuals)

12. Linear Pattern or Not?

13. (residuals have a curve pattern)
Linear Pattern or Not? No
(residuals have a curve pattern)

14. Linear Pattern or Not?

15. Linear Pattern or Not?
YES

16. Page 159, E34

17. Page 159, E34
a) Find the equation of the least squares line for predicting graduation rate from student/faculty ratio.
What is explanatory variable?
What is response variable?

18. Page 159, E34
a) Find the equation of the least squares line for predicting graduation rate from student/faculty ratio.
What is explanatory variable?
What is response variable?

19. Page 159, E34 a) graduation rate =
y-intercept + slope (student/faculty ratio)

20. Page 159, E34 a) graduation rate =
y-intercept + slope (student/faculty ratio)
Slope:

21. Page 159, E34 a) graduation rate =
y-intercept + slope (student/faculty ratio)
Slope:
b1 = (-0.5) =

22. Page 159, E34
To find the y-intercept, use the fact that the point of averages (11.7, 0.827) is on the regression line.

23. Page 159, E34
To find the y-intercept, use the fact that the point of averages (11.7, 0.827) is on the regression line.
y = a + bx
0.827 = a + ( )(11.7)
intercept = ?

24. Page 159, E34
To find the y-intercept, use the fact that the point of averages (11.7, 0.827) is on the regression line.
y = a + bx
0.827 = a + ( )(11.7)
intercept =

25. Page 159, E34
graduation rate =
0.94 – (student/faculty ratio)

26. Page 159, E34
b) Find the equation of the least squares line for predicting student/faculty ratio from graduation rate.

27. Page 159, E34(b) student/faculty ratio =
y-intercept + slope(graduation rate)

28. Page 159, E34(b) student/faculty ratio =
y-intercept + slope(graduation rate)
Slope:

29. Page 159, E34(b) student/faculty ratio =
y-intercept + slope(graduation rate)
Slope:

30. Page 159, E34(b)
To find the y-intercept, use the fact that the point of averages (0.827, 11.7) is on the regression line.
y = a + bx
11.7 = a + (-25.90)(0.827)
intercept = ?

31. Page 159, E34(b)
To find the y-intercept, use the fact that the point of averages (0.827, 11.7) is on the regression line.
y = a + bx
11.7 = a + (-25.9)(0.827)
intercept = 33.12

32. Page 159, E34(b)
student/faculty ratio =
33.12 – 25.9(graduation rate)

33. Page 159, E34(b) a) graduation rate =
0.94 – (student/faculty ratio)
b) student/faculty ratio =
33.12 – 25.9(graduation rate)

34. Page 160, E37(b)

35. Page 160, E37(b)
b. If we kept the price of cheeseburgers down, college would be more affordable.
Lurking variable?

36. Page 160, E37(b)
b. If we kept the price of cheeseburgers down, college would be more affordable.
The lurking variable is inflation over the years—all costs have gone up over the years.

37. Page 177, E47
a) Use your calculator to create a residual plot for this data.

38. Page 177, E47

39. Page 177, E47b Which pizza has largest positive residual?
Which pizza has largest negative residual?

40. Page 177, E47b Which pizza has largest positive residual?
Which pizza has largest negative residual?

41. Page 177, E47b Which pizza has largest positive residual?
Pizza Hut’s Stuffed Crust
Which pizza has largest negative residual?

42. Page 177, E47b
Which pizza has largest negative residual?

43. Page 177, E47b
Which pizza has largest negative residual?

44. Page 177, E47b Which pizza has largest negative residual?
Pizza Hut’s Pan

45. Page 177, E47b
Are any of these residuals so extreme as to suggest that those pizzas should be regarded as extreme?

46. Page 177, E47b
Are any of these residuals so extreme as to suggest that those pizzas should be regarded as extreme?
Make a modified boxplot of the residuals to check for outliers.

47. Page 177, E47b
Are any of these residuals so extreme as to suggest that those pizzas should be regarded as extreme?
No residuals are outliers so no pizza should be regarded as extreme.

48. Page 177, E49

49. Page 177, E49
A. I
B. IV
C. III
D. II

50. Page 177, E49
Linear model would be appropriate for
C and D.

51. Page 178, E51(a)

52. Page 178, E51(a) a) The regression equation is
cost = (seats).

53. Questions?
Be certain to bring your book!