1. Section 11.1
Day 3

2. Page 752, E2

3. Page 752, E2
a. For each pair of variables, tell whether you think a line gives a suitable summary of the relationship.

4. Mean Gas versus Mean Temp

5. Mean Gas versus Mean Temp
A line is appropriate at least for values of x of 65°F or less.
There is no obvious curvature, and the variation around the line is fairly uniform.
The points around 70 degrees vary less than the points at the other temperatures and appear to be approaching the horizontal limit of 0.

6. Mean KWH versus Mean Temp

7. Mean KWH versus Mean Temp
There appears to be no curvature.
A line can be used as a summary of the relationship, but there is more variation in the responses at the lower values of x
than at the higher (i.e., lack of homogeneity).

8. Mean KWH versus Heat DD

9. Mean KWH versus Heat DD
No, this plot shows that this is not a good data set for supporting a linear regression model.
Although the data show a slight positive trend, the variation in responses is too great at the larger values of x (Heat DD) for
inferential techniques to be correct or useful.

10. Heat DD versus Mean Temp

11. Heat DD versus Mean Temp
This plot appears to be quite linear, but

12. Heat DD versus Mean Temp
Residuals vs Mean Temp

13. Heat DD versus Mean Temp
This plot appears to be quite linear, but a residual plot shows pronounced curvature. It appears that the relationship between these variables is not linear.
Again, the problem appears to be with points with values of x greater than 65°F.

14. Page 752, E2
b. By looking at the scatterplots, estimate which of the four pairs of variables has the largest standard error of the slope and which has the smallest.

15. Key Concept
The slope b1 of the regression line varies less from sample to sample when:
Sample size is larger
Residuals are smaller
Values of x are further apart

16. Page 752, E2
b. By looking at the scatterplots, estimate which of the four pairs of variables has the largest standard error of the slope and which has the smallest.

18. Page 752, E2
b. Note: Look at the units to determine the approximate residuals and spread in x-values and, therefore, the approximate standard error.

20. largest standard error of the slope

21. smallest standard error of the slope
largest standard error of the slope

22. Page 752, E2 c. Compute the slope of the LSRL for the
relationship between y = Mean Gas and
x = Mean Temp.
Interpret the slope in context.
Compute the estimated standard error of the slope.

23. Page 752, E2 c. The estimated slope is - 0.23643.
Interpret? Look at descriptions of variables

24. Page 752, E2 c. The estimated slope is - 0.23643.
If one month has a mean daily temperature that is 1°F higher than another month, its mean daily gas usage tends to be therms less.

25. Page 752, E2
The standard error of the slope is:

26. Page 752, E2
The standard error of the slope is:

27. Page 752, E2

28. Page 752, E2 b1?

29. Page 752, E2 b1

30. Page 752, E2 b0? b1

31. Page 752, E2 b0 b1

32. Page 752, E2 sb1? b0 b1

33. Page 752, E2 b0 b1
sb1

34. Page 752, E2 s? b0 b1
sb1

35. Page 752, E2 b0 b1
sb1

36. Page 752, E2 Here, s is the estimate of the common
variability in the mean natural gas usage
daily for the month for each fixed
temperature.

37. Page 749, P3

38. Page 749, P3

39. Page 749, P3

40. Page 749, P3

41. Page 749, P3

42. Page 754, E5

43. Page 754, E5 a. The soil samples should have the larger
variability in the slope because the distance
of y from the regression line tends to be
larger compared to the spread in x.

44. Page 754, E5 The standard error for the soil samples is 0.36165.
From P6, the standard error for the rock
samples was
As predicted, the standard error for the
soil samples is much larger.

45. Page 754, E6

46. Page 754, E6 a. After the outlying point is removed, the
remaining points all fall close to a line, so the
variation in the residuals will decrease.
Because the variation in the x-values will not
change much, this implies that the standard error
of the slope will also decrease.
So, you expect the estimated standard
error of the slope to be larger for the ______ data.

47. Page 754, E6 a. After the outlying point is removed, the
remaining points all fall close to a line, so the
variation in the residuals will decrease.
Because the variation in the x-values will not
change much, this implies that the standard error
of the slope will also decrease.
So, you expect the estimated standard
error of the slope to be larger for the original data.

48. Page 754, E6

49. Questions?