1. Section 11.2
Day 3

2. Using computer printouts to:
Write equation for LSRL

3. Using computer printouts to:
Write equation for LSRL
Write conclusion for significance test of slope

4. Using computer printouts to:
Write equation for LSRL
Write conclusion for significance test of slope
Construct confidence interval for slope

5. Page 761
t, not t*
s is standard deviation of residuals (variability around regression line)

6. Page 761
1) Write equation for LSRL

7. y = b0 + b1x
1) Write equation for LSRL

8. y = b0 + b1x
1) Price = horsepower

9. 2) Let Ho: = 0, there is no linear relationship between horsepower and price of a car;
Ha:

10. 2) Let Ho: = 0, there is no linear relationship between horsepower and price of a car; Ha: What is conclusion for 2-sided significance test of slope?

11. 2) We reject the null hypothesis because the P-value of 0
2) We reject the null hypothesis because the P-value of is less than the significance level of = 0.05.

12. 2) We reject the null hypothesis because the P-value of 0
2) We reject the null hypothesis because the P-value of is less than the significance level of = 0.05.
Thus, there is sufficient evidence to support the claim that a positive linear relationship exists between horsepower and the price of a car.

13. Page 768, P15

14. Page 768, P15
Construct a 90% confidence interval for the true slope.

15. To find confidence interval for slope use:

16. To find confidence interval for slope use:

17. To find confidence interval for slope use:

18. Page 768, P15
Construct a 90% confidence interval for the true slope. t* = (from Table B)

19. Page 768, P15 Construct a 90% confidence interval for the true slope.
= (0.0039)

20. Page 768, P15
Construct a 90% confidence interval for the true slope.
= (0.0039)
( , )
Interpret CI?

21. Page 768, P15
( , )
I’m 90% confident that the slope of the true regression line for predicting titanium dioxide content from silicon dioxide content for Mars rocks is in the interval to

22. Page 768, P15
b) What does the value s = tell you?

23. Page 768, P15 b. The value s = 0.0257 is an estimate of , the
standard deviation of the errors from the true
regression line.
In other words, it is an estimate of a typical
distance of the points from that line.

24. Page 766, P13
a. Fit a straight line to the data that could be used to predict the temperature from the chirp rate. Interpret the slope.

25. Page 766, P13

26. Page 766, P13

27. LSRL equation:

28. Page 766, P13
temperature = chirps/sec
Interpret slope.

29. Page 766, P13 a) temperature = 25.232 + 3.291 chirps/sec
If the number of chirps per second increases by 1, we can expect the temperature to increase by about 3.291o F.

30. Page 766, P13
b) Make residual plot (chirp rate, residual).

31. Page 766, P13
b) Make residual plot (chirp rate, residual).

32. Page 766, P13 b)

33. Page 766, P13 The residual plot shows no obvious pattern,
so a linear model fits the data well.
There is little evidence that the residuals
tend to change in size as x increases.

34. Page 766, P13
b. Make a plot of the residuals

35. Page 766, P13

36. Page 766, P13 The plot of the residuals is fairly symmetric
with no outliers. So reasonable to assume
residuals came from normal distribution.

37. Page 766, P13
Have we checked all the conditions we should check?

38. Page 766, P13 Have we checked all the conditions we should check?
No. Randomness: We can not tell if this was a random sample of cricket chirping.

39. Page 766, P13
c) Perform a two-sided LinRegTTest to determine t and a P-value.
Name:

40. Page 766, P13
c) Perform a two-sided LinRegTTest to determine t and a P-value.
Name: Two-sided significance test for a slope
Hypotheses?

41. Page 766, P13 c)
Ho: = 0, there is no linear relationship between rate of chirping and temperature.
Ha:

42. Page 766, P13 c)
t = 5.47
P-value =

43. Page 766, P13
c) t = 5.47; P-value =

44. Page 766, P13
Conclusion?

45. Page 766, P13 I reject the null hypothesis because
the P-value of is less than the
significance level of 0.05.
There is sufficient evidence to support the claim that there is a linear relationship between the rate of chirping and the air temperature.
This conclusion depends on having a random sample of cricket chirping.

46. Page 769, E14

47. Page 769, E14
Name:

48. Page 769, E14
Name: Two-sided significance test for a slope

49. Conditions

50. Page 769, E14 Randomness: The months were not randomly selected.
These are the available monthly records in Boston for a gas-heated single-family residence with no air conditioning.

51. Page 769, E14
Linearity: The scatterplot shows a fairly symmetric linear trend.

52. Page 769, E14
Uniform residuals: The residual plot shows that the variation in mean electricity usage tends to get smaller as the mean temperature increases.

53. Page 769, E14
Normality: The boxplot of the residuals is fairly symmetric so the residuals look as if the residuals reasonably could have come from a normally distributed population although there is an outlier.

54. Page 769, E14
Based on the conditions, what should we do?

55. Page 769, E14 Based on the conditions, what should we do?
Continue with the test, but be cautious in drawing a conclusion. Include caveat about not being a random sample.

56. Hypotheses

57. Hypotheses
Ho: β1 = 0, where β1 is the slope of the true linear relationship between mean monthly temperature and mean monthly electricity usage.

58. Hypotheses
Ho: β1 = 0, where β1 is the slope of the true linear relationship between mean monthly temperature and mean monthly electricity usage. Ha: β1 ≠ 0

59. Page 769, E14
t = ± 2.708
P-value =

60. Page 769, E14 I reject the null hypothesis because the
P-value of is less than the
significance level of 0.05.

61. Page 769, E14 I reject the null hypothesis because the
P-value of is less than the
Significance level of 0.05.
If this were a random sample, there would
be sufficient evidence to support the claim
that the slope of the true linear relationship
between mean monthly temperature and
mean monthly electricity usage is not 0.

62. Page 769, E14
b) Strong evidence of a linear relationship or evidence of a strong linear relationship? Why?

63. Page 769, E14
b) Strong evidence of a linear relationship or evidence of a strong linear relationship? Why?

64. Page 769, E14
b) Strong evidence of a linear relationship or evidence of a strong linear relationship? Why?
This is strong evidence of a linear
relationship, but because r is not very close
to -1 or 1 (it is 0.538), the relationship is not
strong.

65. Questions?