1. Section 11.2
Day 4

2. Tomorrow: Quiz 11.1 – May use all your notes -- May use your book -- Must work in a group of at least 4 -- all must be engaged in working & discussing the problems

3. Wednesday – 11.1 – 11.2 Homework Quiz Thursday –
Extra credit Fathom lab due
Test 11.1 – 11.2
-- both sides of 1 note card

4. Friday
– not free time to waste
- work on semester final review packet

5. Page 769, E14

6. Page 769, E14
Name:

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

8. Conditions

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Randomness:

10. 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.

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Linearity:

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Linearity: The scatterplot shows a fairly symmetric linear trend.

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Uniform residuals:

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

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Normality:

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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.

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Based on the conditions, what should we do?

18. 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.

19. Hypotheses

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

21. 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

22. Computations

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

24. Conclusion

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

26. 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.

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

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b) Strong evidence of a linear relationship or evidence of a strong linear relationship? Why?

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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.

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31. Page 769, E15

32. Page 769, E15 Do we use this printout for predicting the:
(i) temperature from chirp rate or
(ii) chirp rate from temperature?

33. Page 769, E15 Do we use this printout for predicting the:
(i) temperature from chirp rate or
(ii) chirp rate from temperature?

34. Construct a 95% CI for the slope of the true regression line.

35. Page 769, E15

36. Page 769, E15 A 95% confidence interval is 1.9925 to 4.5897.
Interpretation:
I’m 95% confident that the slope of the
true regression line for predicting the
temperature from the chirp rate is in the
interval to

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ii. 95% CI for predicting chirp rate from temperature

38. Page 769, E15

39. Page 769, E15 A 95% confidence interval is 0.12831 to 0.29553.
I’m 95% confident that the slope of the true regression line for predicting chirp rate from temperature is in the interval to

40. Page 769, E15

41. Questions?