Question 1

When using the least squares method,the column of residuals always sums to zero.

Accepted Answer

A) True 
 B)False

Question 2

A poor prediction (large residual)indicates an observation with high leverage.

Accepted Answer

A) True 
 B)False

Question 3

"High leverage" would refer to a data point that is poorly predicted by the model (large residual).

Accepted Answer

A) True 
 B)False

Question 4

In a simple bivariate regression with 60 observations there will be _____ residuals.

Accepted Answer

A)  60 
B)  59 
C)  58 
D)  57 
A)  60 
B)  59 
C)  58 
D)  57

Question 5

The correlation coefficient r always has the same sign as b1 in Y = b0 + b1X.

Accepted Answer

A) True 
 B)False

Question 6

High leverage for an observation indicates that X is far from its mean.

Accepted Answer

A) True 
 B)False

Question 7

Autocorrelated errors are not usually a concern for regression models using cross-sectional data.

Accepted Answer

A) True 
 B)False

Question 8

A predictor that is significant in a one-tailed t-test will also be significant in a two-tailed test at the same level of significance α.

Accepted Answer

A) True 
 B)False

Question 9

The ordinary least squares (OLS)method of estimation will minimize:

Accepted Answer

A)  neither the slope nor the intercept. 
B)  only the slope. 
C)  only the intercept. 
D)  both the slope and intercept. 
A)  neither the slope nor the intercept. 
B)  only the slope. 
C)  only the intercept. 
D)  both the slope and intercept.

Question 10

An observation with high leverage will have a large residual (usually an outlier).

Accepted Answer

A) True 
 B)False

Question 11

Which of the following is not a characteristic of the F-test in a simple regression?

Accepted Answer

A)  It is a test for overall fit of the model. 
B)  The test statistic can never be negative. 
C)  It requires a table with numerator and denominator degrees of freedom. 
D)  The F-test gives a different p-value than the t-test. 
A)  It is a test for overall fit of the model. 
B)  The test statistic can never be negative. 
C)  It requires a table with numerator and denominator degrees of freedom. 
D)  The F-test gives a different p-value than the t-test.

Question 12

The ordinary least squares method of estimation minimizes the estimated slope and intercept.

Accepted Answer

A) True 
 B)False

Question 13

Which is not correct regarding the estimated slope of the OLS regression line?

Accepted Answer

A)  It is divided by its standard error to obtain its t statistic. 
B)  It shows the change in Y for a unit change in X. 
C)  It is chosen so as to minimize the sum of squared errors. 
D)  It may be regarded as zero if its p-value is less than α. 
A)  It is divided by its standard error to obtain its t statistic. 
B)  It shows the change in Y for a unit change in X. 
C)  It is chosen so as to minimize the sum of squared errors. 
D)  It may be regarded as zero if its p-value is less than α.

Question 14

Pearson's correlation coefficient (r)requires that both variables be interval or ratio data.

Accepted Answer

A) True 
 B)False

Question 15

When comparing the 90 percent prediction and confidence intervals for a given regression analysis:

Accepted Answer

A)  the prediction interval is narrower than the confidence interval. 
B)  the prediction interval is wider than the confidence interval. 
C)  there is no difference between the size of the prediction and confidence intervals. 
D)  no generalization is possible about their comparative width. 
A)  the prediction interval is narrower than the confidence interval. 
B)  the prediction interval is wider than the confidence interval. 
C)  there is no difference between the size of the prediction and confidence intervals. 
D)  no generalization is possible about their comparative width.

Question 16

A prediction interval for Y is widest when X is near its mean.

Accepted Answer

A) True 
 B)False

Question 17

In a sample of n = 40,a sample correlation of r = .400 provides sufficient evidence to conclude that the population correlation coefficient exceeds zero in a right-tailed test at:

Accepted Answer

A)  α = .025 but not α = .05. 
B)  α = .05 but not α = .025. 
C)  both α = .025 and α = .05. 
D)  neither α = .025 nor α = .05. 
A)  α = .025 but not α = .05. 
B)  α = .05 but not α = .025. 
C)  both α = .025 and α = .05. 
D)  neither α = .025 nor α = .05.

Question 18

In a simple regression Y = b0 + b1X where Y = number of robberies in a city (thousands of robberies),X = size of the police force in a city (thousands of police),and n = 45 randomly chosen large U.S.cities in 2008,we would be least likely to see which problem?

Accepted Answer

A)  Autocorrelated residuals (because this is time-series data) 
B)  Heteroscedastic residuals (because we are using totals uncorrected for city size) 
C)  Nonnormal residuals (because a few larger cities may skew the residuals) 
D)  High leverage for some observations (because some cities may be huge) 
A)  Autocorrelated residuals (because this is time-series data) 
B)  Heteroscedastic residuals (because we are using totals uncorrected for city size) 
C)  Nonnormal residuals (because a few larger cities may skew the residuals) 
D)  High leverage for some observations (because some cities may be huge)

Question 19

Which is not true of the coefficient of determination?

Accepted Answer

A)  It is the square of the coefficient of correlation. 
B)  It is negative when there is an inverse relationship between X and Y. 
C)  It reports the percent of the variation in Y explained by X. 
D)  It is calculated using sums of squares (e.g. ,SSR,SSE,SST). 
A)  It is the square of the coefficient of correlation. 
B)  It is negative when there is an inverse relationship between X and Y. 
C)  It reports the percent of the variation in Y explained by X. 
D)  It is calculated using sums of squares (e.g. ,SSR,SSE,SST).

Question 20

A sample correlation r = .40 indicates a stronger linear relationship than r = -.60.

Accepted Answer

A) True 
 B)False

When using the least squares method,the column of residuals always sums to zero.

A poor prediction (large residual)indicates an observation with high leverage.

"High leverage" would refer to a data point that is poorly predicted by the model (large residual).

In a simple bivariate regression with 60 observations there will be _____ residuals.

The correlation coefficient r always has the same sign as b₁ in Y = b₀ + b₁X.

High leverage for an observation indicates that X is far from its mean.

Autocorrelated errors are not usually a concern for regression models using cross-sectional data.

A predictor that is significant in a one-tailed t-test will also be significant in a two-tailed test at the same level of significance α.

The ordinary least squares (OLS)method of estimation will minimize:

An observation with high leverage will have a large residual (usually an outlier).

Which of the following is not a characteristic of the F-test in a simple regression?

The ordinary least squares method of estimation minimizes the estimated slope and intercept.

Which is not correct regarding the estimated slope of the OLS regression line?

Pearson's correlation coefficient (r)requires that both variables be interval or ratio data.

When comparing the 90 percent prediction and confidence intervals for a given regression analysis:

A prediction interval for Y is widest when X is near its mean.

In a sample of n = 40,a sample correlation of r = .400 provides sufficient evidence to conclude that the population correlation coefficient exceeds zero in a right-tailed test at:

In a simple regression Y = b₀ + b₁X where Y = number of robberies in a city (thousands of robberies),X = size of the police force in a city (thousands of police),and n = 45 randomly chosen large U.S.cities in 2008,we would be least likely to see which problem?

Which is not true of the coefficient of determination?

A sample correlation r = .40 indicates a stronger linear relationship than r = -.60.

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions and Estimation

One-Sample Hypothesis Tests

Two-Sample Hypothesis Tests

Analysis of Variance

Multiple Regression

Time-Series Analysis

Chi-Square Tests

Nonparametric Tests

Quality Management

Filters

Exam 12: Simple Regression

When using the least squares method,the column of residuals always sums to zero.

A poor prediction (large residual)indicates an observation with high leverage.

"High leverage" would refer to a data point that is poorly predicted by the model (large residual).

In a simple bivariate regression with 60 observations there will be _____ residuals.

The correlation coefficient r always has the same sign as b1 in Y = b0 + b1X.

High leverage for an observation indicates that X is far from its mean.

Autocorrelated errors are not usually a concern for regression models using cross-sectional data.

A predictor that is significant in a one-tailed t-test will also be significant in a two-tailed test at the same level of significance α.

The ordinary least squares (OLS)method of estimation will minimize:

An observation with high leverage will have a large residual (usually an outlier).

Which of the following is not a characteristic of the F-test in a simple regression?

The ordinary least squares method of estimation minimizes the estimated slope and intercept.

Which is not correct regarding the estimated slope of the OLS regression line?

Pearson's correlation coefficient (r)requires that both variables be interval or ratio data.

When comparing the 90 percent prediction and confidence intervals for a given regression analysis:

A prediction interval for Y is widest when X is near its mean.

In a sample of n = 40,a sample correlation of r = .400 provides sufficient evidence to conclude that the population correlation coefficient exceeds zero in a right-tailed test at:

In a simple regression Y = b0 + b1X where Y = number of robberies in a city (thousands of robberies),X = size of the police force in a city (thousands of police),and n = 45 randomly chosen large U.S.cities in 2008,we would be least likely to see which problem?

Which is not true of the coefficient of determination?

A sample correlation r = .40 indicates a stronger linear relationship than r = -.60.

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions and Estimation

One-Sample Hypothesis Tests

Two-Sample Hypothesis Tests

Analysis of Variance

Multiple Regression

Time-Series Analysis

Chi-Square Tests

Nonparametric Tests

Quality Management

Filters

The correlation coefficient r always has the same sign as b₁ in Y = b₀ + b₁X.

In a simple regression Y = b₀ + b₁X where Y = number of robberies in a city (thousands of robberies),X = size of the police force in a city (thousands of police),and n = 45 randomly chosen large U.S.cities in 2008,we would be least likely to see which problem?