Regression

BPS chapter 5

© 2010 W.H. Freeman and Company

Sum of squared errorsWhich least-squares regression line would have a smaller sum of

squared errors (SSE)?

a) The line in Plot A.

b) The line in Plot B.

c) It would be the same for both plots.

ScatterplotsLook at the following scatterplot. What could we say about the

relationship between r and the slope of the regression line?

a) Since a is negative, r must also be negative.

b) Since b is negative, r must also be negative.

c) Since a is positive, r must also be positive.

d) Since b is positive, r must also be positive.

SlopeLook at the following scatterplot. What would be a correct interpretation of the

slope?

a) As we increase our CO content by 1 mg, we increase the tar content by 1.01 mg.

b) As we increase our CO content by 0.66 mg, we increase the tar content by 1.01 mg.

c) As we increase our CO content by 0.66 mg, we increase the tar content by 0.66 mg.

d) As we increase our CO content by 1 mg, we increase the tar content by 0.66 mg.

Regression lineLook at the following least-squares regression line. If a person

increased his/her weight by 10 pounds, by how much (in inches) would one expect to see their waist girth increase?

a) 0.1332

b) 1.332

c) 99.994

d) 1.332 + 9.9994

Regression lineLook at the following least-squares regression line. The Y-intercept

tells us the predicted waist girth for someone weighing how many pounds?

a) 0b) 0.1332c) 9.9994d) Cannot be determined from the graph.

ResidualsLook at the following least-squares regression line. Compare the

squared errors (residuals) from the two Points A and B.

a) Point A’s would be greater than Point B’s.

b) Point A’s would be less than Point B’s.

c) Point A’s would be equal to Point B’s.

d) There is not enough information.

Percent of variation in YWhat percent of the variation in the sisters’ heights can be explained by

the heights of the brothers?

a) 25.64%

b) (0.558)2 = 31.14%

c) 52.7%

d) 55.8%

CorrelationThe correlation between math SAT score and total SAT score is about

r = 0.9935. What is a correct conclusion that could be made?

a) The least-squares regression line of Y on X would have slope = 0.9935.

b) Math SAT scores explain about 98.7% (which is 0.99352) of the variation in the total SAT scores.

c) About 99.35% of the time math SAT scores will accurately predict total SAT scores.

d) Total SAT score is made up of 99.35% of the math SAT score.

ResidualsResidual equals

a)

b)

c)

d)

Residual plotsResidual plots are used to

a) Examine the relationship between two variables.

b) Identify the mean and spread of the residuals.

c) Check for independence of observations.

d) Magnify violations of regression assumptions.

Residual plots (answer)Residual plots are used to

a) Examine the relationship between two variables.

b) Identify the mean and spread of the residuals.

c) Check for independence of observations.

d) Magnify violations of regression assumptions.

Residual plotsThe following are regression assumptions:

1. The relationship between X and Y can be modeled with a straight line.

2. The variation in the Y values does not depend on the value of X (constant variance).

The residual plot shown below indicates the violation of which regression assumption?

a) 1

b) 2

c) Neither

Residual plots (answer)The following are regression assumptions:

1. The relationship between X and Y can be modeled with a straight line.

2. The variation in the Y values does not depend on the value of X (constant variance).

The residual plot shown below indicates the violation of which regression assumption?

a) 1

b) 2

c) Neither

Residual plotsThe following are regression assumptions:

1. The relationship between X and Y can be modeled with a straight line.

2. The variation in the Y values does not depend on the value of X (constant variance).

The residual plot shown below indicates the violation of which regression assumption?

a) 1

b) 2

c) Neither

Residual plots (answer)The following are regression assumptions:

1. The relationship between X and Y can be modeled with a straight line.

2. The variation in the Y values does not depend on the value of X (constant variance).

The residual plot shown below indicates the violation of which regression assumption?

a) 1

b) 2

c) Neither

Correlation or regressionWhich of the following measures the direction and strength of the linear

association between X and Y?

a) Correlation

b) Regression

Correlation or regressionWhich of the following makes no distinction between explanatory and

response variables?

a) Correlation

b) Regression

Correlation or regressionWhich of the following is used for prediction?

a) Correlation

b) Regression

Regression lineA regression line always passes through the point

a)

b)

c)

d)

Correlation and slopeWhich of the following best describes the relationship between

correlation and slope?

a) The correlation of X and Y equals the slope of the regression line modeling the relationship between X and Y.

b) When the correlation between X and Y is zero, the slope of the regression line modeling the relationship between X and Y is negative.

c) The sign of the correlation between X and Y is the same as the sign of the slope of the regression line modeling the relationship between X and Y.

d) The correlation between X and Y is not related to the slope of the regression line modeling the relationship between X and Y.

Regression lineWhich of the following best measures the strength of fit of a regression

line?

a) Correlation coefficient, r.

b) Square of the correlation coefficient, r2.

c) Square root of the correlation coefficient, .r

Regression line (answer)Which of the following best measures the strength of fit of a regression

line?

a) Correlation coefficient, r.

b) Square of the correlation coefficient, r2.

c) Square root of the correlation coefficient, .r

CausationResearchers interviewed a group of women with knee pain awaiting

knee replacement surgery. They also interviewed a group of women from the same geographical area with no knee pain. These researchers reported that wearing high-heeled shoes caused the knee pain which required surgery. As a savvy consumer of statistics, you conclude that:

a) Because this was only an observational study, the researchers should not make claims that the knee pain was caused by high heels.

b) Because the study was a valid experiment, the researchers were valid in their claim about high heels causing pain.

Linear regressionThe following graph indicates the presence of

a) Extrapolation.

b) An influential observation.

c) A lurking variable.

Linear regressionThe following graph shows the linear relationship between diamond

size and price for diamonds size 0.35 carats or less. Using this relationship to predict the price of a diamond that is 1 carat is considered

a) Extrapolation.b) An influential observation.c) Prediction.

Linear regressionThe diamonds mentioned in the previous question were of the same

cut and clarity. If diamonds of different cuts have different relationship between size and price, we would say that

a) Type of cut is a lurking variable.

b) Type of cut is a confounded variable.

c) Type of cut should be ignored.

Linear regression (answer)The diamonds mentioned in the previous question were of the same

cut and clarity. If diamonds of different cuts have different relationship between size and price, we would say that

a) Type of cut is a lurking variable.

b) Type of cut is a confounded variable.

c) Type of cut should be ignored.