Section 11.2 Day 4
Tomorrow: Quiz 11.1 – 11.2 -- 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
Wednesday – 11.1 – 11.2 Homework Quiz Thursday – Extra credit Fathom lab due Test 11.1 – 11.2 -- both sides of 1 note card
Friday – not free time to waste - work on semester final review packet
Page 769, E14
Page 769, E14 Name:
Page 769, E14 Name: Two-sided significance test for a slope
Conditions
Page 769, E14 Randomness:
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.
Page 769, E14 Linearity:
Page 769, E14 Linearity: The scatterplot shows a fairly symmetric linear trend.
Page 769, E14 Uniform residuals:
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.
Page 769, E14 Normality:
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.
Page 769, E14 Based on the conditions, what should we do?
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.
Hypotheses
Hypotheses Ho: β1 = 0, where β1 is the slope of the true linear relationship between mean monthly temperature and mean monthly electricity usage.
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
Computations
Page 769, E14 t = ± 2.708 P-value = 0.0144
Conclusion
Page 769, E14 I reject the null hypothesis because the P-value of 0.0144 is less than the significance level of 0.05.
Page 769, E14 I reject the null hypothesis because the P-value of 0.0144 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.
Page 769, E14 b) Strong evidence of a linear relationship or evidence of a strong linear relationship? Why?
Page 769, E14 b) Strong evidence of a linear relationship or evidence of a strong linear relationship? Why?
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.
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Page 769, E15
Page 769, E15 Do we use this printout for predicting the: (i) temperature from chirp rate or (ii) chirp rate from temperature?
Page 769, E15 Do we use this printout for predicting the: (i) temperature from chirp rate or (ii) chirp rate from temperature?
Construct a 95% CI for the slope of the true regression line.
Page 769, E15
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 1.9925 to 4.5897
Page 769, E15 ii. 95% CI for predicting chirp rate from temperature
Page 769, E15
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 0.12831 to 0.29553.
Page 769, E15
Questions?