Inference for Regression

BPS chapter 23

© 2010 W.H. Freeman and Company

1. Hypothesis testsResearchers at The Ohio State University wanted to know if they could

use the number of beers consumed by a student to predict the student’s blood alcohol content (BAC). The following scatter plot shows the data. From the scatter plot it appears that there is ___ correlation between number of beers and BAC.

a) positive

b) negative

c) No

d) All of the above

1. Hypothesis testsResearchers at The Ohio State University wanted to know if they could

use the number of beers consumed by a student to predict the student’s blood alcohol content (BAC). The following scatterplot shows the data. From the scatter plot it appears that there is ___ correlation between number of beers and BAC.

a) positive

b) negative

c) No

d) All of the above

2. Hypothesis testsResearchers at The Ohio State University wanted to know if they could

use the number of beers consumed by a student to predict the student’s blood alcohol content (BAC). In order to know if the number of beers consumed was a good predictor of BAC, they tested . What can we conclude from the following table?

a) Because the P-value is 0.3320, there is a significant linear relationship between the number of beers consumed and BAC.

b) Because the P-value is 0.0000, there is a significant linear relationship between the number of beers consumed and BAC.

c) Because the P-value is 0.3320, there is no significant linear relationship between the number of beers consumed and BAC.

d) Because the P-value is 0.0000, there is no significant linear relationship between the number of beers consumed and BAC.

0 : 0, : 0aH H

2. Hypothesis tests (answer)Researchers at The Ohio State University wanted to know if they could

use the number of beers consumed by a student to predict the student’s blood alcohol content (BAC). In order to know if the number of beers consumed was a good predictor of BAC, they tested . What can we conclude from the following table?

a) Because the P-value is 0.3320, there is a significant linear relationship between the number of beers consumed and BAC.

b) Because the P-value is 0.0000, there is a significant linear relationship between the number of beers consumed and BAC.

c) Because the P-value is 0.3320, there is no significant linear relationship between the number of beers consumed and BAC.

d) Because the P-value is 0.0000, there is no significant linear relationship between the number of beers consumed and BAC.

0 : 0, : 0aH H

3. ConclusionsAn article in a newspaper said that students who major in subjects that

have higher expected incomes after graduation are more likely to be married. This conclusion is:

a) Correct because the data were collected in a scientific way.

b) Incorrect because the results are likely biased due to lurking variables.

c) Not reliable because it does not sound plausible.

3. Conclusions (answer)An article in a newspaper said that students who major in subjects that

have higher expected incomes after graduation are more likely to be married. This conclusion is:

a) Correct because the data were collected in a scientific way.

b) Incorrect because the results are likely biased due to lurking variables.

c) Not reliable because it does not sound plausible.

4. Linear regressionWhich point represents “a” in our least-squares regression equation?

a) Point Q

b) Point S

c) Point R

d) Point T

4. Linear regression (answer)Which point represents “a” in our least-squares regression equation?

a) Point Q

b) Point S

c) Point R

d) Point T

5. CorrelationIf two quantitative variables, X and Y, have a correlation coefficient r =

0.80, which graph could be a scatterplot of the two variables?

a) Plot A

b) Plot B

c) Plot C

5. Correlation (answer)If two quantitative variables, X and Y, have a correlation coefficient r =

0.80, which graph could be a scatterplot of the two variables?

a) Plot A

b) Plot B

c) Plot C

6. ResidualThe following scatterplot shows the number of gold medals earned by

countries in 1992 versus how many earned in 1996. Which of the points would have the smallest residual?

a) Point Ab) Point Bc) Point Cd) Point D

6. Residual (answer)The following scatterplot shows the number of gold medals earned by

countries in 1992 versus how many earned in 1996. Which of the points would have the smallest residual?

a) Point Ab) Point Bc) Point Cd) Point D

8. Appropriate analysisEdwin Hubble collected data on the distance a galaxy is from the earth

and the velocity with which it appears to be receding. If he wanted to investigate if there was a linear relationship between the distance and the velocity, what type of analysis did he perform?

a) Two-sample t-test on means

) 2 analysis on proportions

c) Linear regression analysis

d) Matched pairs experiment

8. Appropriate analysis (answer)Edwin Hubble collected data on the distance a galaxy is from the earth

and the velocity with which it appears to be receding. If he wanted to investigate if there was a linear relationship between the distance and the velocity, what type of analysis did he perform?

a) Two-sample t-test on means

) 2 analysis on proportions

c) Linear regression analysis

d) Matched pairs experiment

9. Linear regressionEdwin Hubble collected data on the distance a galaxy is from the earth

and the velocity with which it appears to be receding. He used the following model: where x represents the distance the galaxy is from the earth (in megaparsecs) and represents the mean velocity (in km/sec) for all galaxies at that distance. What does represent in this problem?

a) The average velocity for a galaxy that is extremely close to earth.

b) The average change in velocity for a one-megaparsec increase in distance for those galaxies in the sample.

c) The average velocity for all galaxies in the universe.

d) The average change in velocity for a one-megaparsec increase in distance of all galaxies.

y x y

9. Linear regression (answer)Edwin Hubble collected data on the distance a galaxy is from the earth

and the velocity with which it appears to be receding. He used the following model: where x represents the distance the galaxy is from the earth (in megaparsecs) and represents the mean velocity (in km/sec) for all galaxies at that distance. What does represent in this problem?

a) The average velocity for a galaxy that is extremely close to earth.

b) The average change in velocity for a one-megaparsec increase in distance for those galaxies in the sample.

c) The average velocity for all galaxies in the universe.

d) The average change in velocity for a one-megaparsec increase in distance of all galaxies.

y x y

10. Linear regressionEdwin Hubble collected data on the distance a galaxy is from the earth

and the velocity with which it appears to be receding. Summarizing his data with a scatterplot and generating the least-squares regression line gave the following table:

Based on the information in the table, what is the correct equation for the least-squares regression line?

a)

b)

c)

d)

e)

10. Linear regression (answer)Edwin Hubble collected data on the distance a galaxy is from the earth

and the velocity with which it appears to be receding. Summarizing his data with a scatterplot and generating the least-squares regression line gave the following table:

Based on the information in the table, what is the correct equation for the least-squares regression line?

a)

b)

c)

d)

e)

11. ResidualsEdwin Hubble collected data on the distance a galaxy is from the earth and the

velocity with which it appears to be receding. By looking at the following residual plot and histogram of the residuals, what conclusion should be made about the conditions for performing the linear regression?

a) Because the residual plot shows no pattern and the histogram is approximately bell-shaped, the conditions are met.

b) The residual plot implies that the data violate the assumption of normality.c) The histogram of the residuals shows that the data are extremely right-

skewed.d) Neither plot tells us anything about the assumptions for doing inference for

regression.e) The residual plot implies that the data violate the assumption of linearity.

11. Residuals (answer)Edwin Hubble collected data on the distance a galaxy is from the earth and the

velocity with which it appears to be receding. By looking at the following residual plot and histogram of the residuals, what conclusion should be made about the conditions for performing the linear regression?

a) Because the residual plot shows no pattern and the histogram is approximately bell-shaped, the conditions are met.

b) The residual plot implies that the data violate the assumption of normality.c) The histogram of the residuals shows that the data are extremely right-

skewed.d) Neither plot tells us anything about the assumptions for doing inference for

regression.e) The residual plot implies that the data violate the assumption of linearity.

12. Linear relationshipEdwin Hubble collected data on the distance a galaxy is from the earth

and the velocity with which it appears to be receding. If the researchers want to test whether there is a positive linear relationship between the distance and velocity, what hypotheses could be used?

a)

b)

c)

d)

12. Linear relationship (answer)Edwin Hubble collected data on the distance a galaxy is from the earth

and the velocity with which it appears to be receding. If the researchers want to test whether there is a positive linear relationship between the distance and velocity, what hypotheses could be used?

a)

b)

c)

d)

13. RelationshipsThe following plot shows a person’s score on a sobriety test versus

their blood alcohol content. Which statement is NOT true about this plot?

a) An outlier is present in the dataset.

b) A relationship exists between BAC and the test score.

c) The relationship could be modeled with a straight line.

d) There is a positive relationship between the two variables.

13. Relationships (answer)The following plot shows a person’s score on a sobriety test versus

their blood alcohol content. Which statement is NOT true about this plot?

a) An outlier is present in the dataset.

b) A relationship exists between BAC and the test score.

c) The relationship could be modeled with a straight line.

d) There is a positive relationship between the two variables.

14. ConclusionsThe average height of people in the United States has been increasing

for decades. Similarly there is evidence that the number of plant species is decreasing over these decades. An appropriate conclusion to draw from these observations would be that

a) Even though they appear to be associated, we could not conclude association.

b) Growing adults are causing the number of plant species to decrease.

c) There is a positive relationship between the two variables.

14. Conclusions (answer)The average height of people in the United States has been increasing

for decades. Similarly there is evidence that the number of plant species is decreasing over these decades. An appropriate conclusion to draw from these observations would be that

a) Even though they appear to be associated, we could not conclude association.

b) Growing adults are causing the number of plant species to decrease.

c) There is a positive relationship between the two variables.