Question 1

Which is indicative of an inverse relationship between X and Y?

Accepted Answer

A)  A negative F statistic 
B)  A negative p-value for the correlation coefficient 
C)  A negative correlation coefficient 
D)  Either a negative F statistic or a negative p-value 
A)  A negative F statistic 
B)  A negative p-value for the correlation coefficient 
C)  A negative correlation coefficient 
D)  Either a negative F statistic or a negative p-value

Question 2

The larger the absolute value of the t statistic of the slope in a simple linear regression,the stronger the linear relationship exists between X and Y.

Accepted Answer

A) True 
 B)False

Question 3

In least-squares regression,the residuals e1,e2,... ,en will always have a zero mean.

Accepted Answer

A) True 
 B)False

Question 4

In correlation analysis,neither X nor Y is designated as the independent variable.

Accepted Answer

A) True 
 B)False

Question 5

A prediction interval for Y is narrower than the corresponding confidence interval for the mean of Y.

Accepted Answer

A) True 
 B)False

Question 6

The critical value for a two-tailed test of H0: β1 = 0 at α = .05 in a simple regression with 22 observations is:

Accepted Answer

A)  ±1.725 
B)  ±2.086 
C)  ±2.528 
D)  ±1.960 
A)  ±1.725 
B)  ±2.086 
C)  ±2.528 
D)  ±1.960

Question 7

If SSR is 1800 and SSE is 200,then R2 is .90.

Accepted Answer

A) True 
 B)False

Question 8

In a sample of n = 23,the critical value of Student's t for a two-tailed test of significance for a simple bivariate regression at α = .05 is:

Accepted Answer

A)  ±2.229 
B)  ±2.819 
C)  ±2.646 
D)  ±2.080 
A)  ±2.229 
B)  ±2.819 
C)  ±2.646 
D)  ±2.080

Question 9

In a simple regression,which would suggest a significant relationship between X and Y?

Accepted Answer

A)  Large p-value for the estimated slope 
B)  Large t statistic for the slope 
C)  Large p-value for the F statistic 
D)  Small t-statistic for the slope 
A)  Large p-value for the estimated slope 
B)  Large t statistic for the slope 
C)  Large p-value for the F statistic 
D)  Small t-statistic for the slope

Question 10

William used a sample of 68 large U.S.cities to estimate the relationship between Crime (annual property crimes per 100,000 persons)and Income (median annual income per capita,in dollars).His estimated regression equation was Crime = 428 + 0.050 Income.We can conclude that:

Accepted Answer

A)  the slope is small so Income has no effect on Crime. 
B)  crime seems to create additional income in a city. 
C)  wealthy individuals tend to commit more crimes,on average. 
D)  the intercept is irrelevant since zero median income is impossible in a large city. 
A)  the slope is small so Income has no effect on Crime. 
B)  crime seems to create additional income in a city. 
C)  wealthy individuals tend to commit more crimes,on average. 
D)  the intercept is irrelevant since zero median income is impossible in a large city.

Question 11

A standardized residual ei = -2.205 indicates:

Accepted Answer

A)  a rather poor prediction. 
B)  an extreme outlier in the residuals. 
C)  an observation with high leverage. 
D)  a likely data entry error. 
A)  a rather poor prediction. 
B)  an extreme outlier in the residuals. 
C)  an observation with high leverage. 
D)  a likely data entry error.

Question 12

For a regression with 200 observations,we expect that about 10 residuals will exceed two standard errors.

Accepted Answer

A) True 
 B)False

Question 13

A local trucking company fitted a regression to relate the travel time (days)of its shipments as a function of the distance traveled (miles).The fitted regression is Time = -7.126 + .0214 Distance,based on a sample of 20 shipments.The estimated standard error of the slope is 0.0053.Find the critical value for a right-tailed test to see if the slope is positive,using α = .05.

Accepted Answer

A)  2.101 
B)  2.552 
C)  1.960 
D)  1.734 
A)  2.101 
B)  2.552 
C)  1.960 
D)  1.734

Question 14

In a sample of size n = 23,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 = .01 but not α = .05. 
B)  α = .05 but not α = .01. 
C)  both α = .05 and α = .01. 
D)  neither α = .05 nor α = .01. 
A)  α = .01 but not α = .05. 
B)  α = .05 but not α = .01. 
C)  both α = .05 and α = .01. 
D)  neither α = .05 nor α = .01.

Question 15

A news network stated that a study had found a positive correlation between the number of children a worker has and his or her earnings last year.You may conclude that:

Accepted Answer

A)  people should have more children so they can get better jobs. 
B)  the data are erroneous because the correlation should be negative. 
C)  causation is in serious doubt. 
D)  statisticians have small families. 
A)  people should have more children so they can get better jobs. 
B)  the data are erroneous because the correlation should be negative. 
C)  causation is in serious doubt. 
D)  statisticians have small families.

Question 16

In a simple regression,if the coefficient for X is positive and significantly different from zero,then an increase in X is associated with an increase in the mean (i.e. ,the expected value)of Y.

Accepted Answer

A) True 
 B)False

Question 17

Confidence intervals for predicted Y are less precise when the residuals are very small.

Accepted Answer

A) True 
 B)False

Question 18

A negative value for the correlation coefficient (r)implies a negative value for the slope (b1).

Accepted Answer

A) True 
 B)False

Question 19

Two-tailed t-tests are often used because any predictor that differs significantly from zero in a two-tailed test will also be significantly greater than zero or less than zero in a one-tailed test at the same α.

Accepted Answer

A) True 
 B)False

Question 20

The coefficient of determination is the percentage of the total variation in the response variable Y that is explained by the predictor X.

Accepted Answer

A) True 
 B)False

Which is indicative of an inverse relationship between X and Y?

The larger the absolute value of the t statistic of the slope in a simple linear regression,the stronger the linear relationship exists between X and Y.

In least-squares regression,the residuals e₁,e₂,... ,e_n will always have a zero mean.

In correlation analysis,neither X nor Y is designated as the independent variable.

A prediction interval for Y is narrower than the corresponding confidence interval for the mean of Y.

The critical value for a two-tailed test of H₀: β₁ = 0 at α = .05 in a simple regression with 22 observations is:

If SSR is 1800 and SSE is 200,then R² is .90.

In a sample of n = 23,the critical value of Student's t for a two-tailed test of significance for a simple bivariate regression at α = .05 is:

In a simple regression,which would suggest a significant relationship between X and Y?

William used a sample of 68 large U.S.cities to estimate the relationship between Crime (annual property crimes per 100,000 persons)and Income (median annual income per capita,in dollars).His estimated regression equation was Crime = 428 + 0.050 Income.We can conclude that:

A standardized residual e_i = -2.205 indicates:

For a regression with 200 observations,we expect that about 10 residuals will exceed two standard errors.

In a sample of size n = 23,a sample correlation of r = .400 provides sufficient evidence to conclude that the population correlation coefficient exceeds zero in a right-tailed test at:

A news network stated that a study had found a positive correlation between the number of children a worker has and his or her earnings last year.You may conclude that:

In a simple regression,if the coefficient for X is positive and significantly different from zero,then an increase in X is associated with an increase in the mean (i.e. ,the expected value)of Y.

Confidence intervals for predicted Y are less precise when the residuals are very small.

A negative value for the correlation coefficient (r)implies a negative value for the slope (b₁).

Two-tailed t-tests are often used because any predictor that differs significantly from zero in a two-tailed test will also be significantly greater than zero or less than zero in a one-tailed test at the same α.

The coefficient of determination is the percentage of the total variation in the response variable Y that is explained by the predictor X.

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

Which is indicative of an inverse relationship between X and Y?

The larger the absolute value of the t statistic of the slope in a simple linear regression,the stronger the linear relationship exists between X and Y.

In least-squares regression,the residuals e1,e2,... ,en will always have a zero mean.

In correlation analysis,neither X nor Y is designated as the independent variable.

A prediction interval for Y is narrower than the corresponding confidence interval for the mean of Y.

The critical value for a two-tailed test of H0: β1 = 0 at α = .05 in a simple regression with 22 observations is:

If SSR is 1800 and SSE is 200,then R2 is .90.

In a sample of n = 23,the critical value of Student's t for a two-tailed test of significance for a simple bivariate regression at α = .05 is:

In a simple regression,which would suggest a significant relationship between X and Y?

William used a sample of 68 large U.S.cities to estimate the relationship between Crime (annual property crimes per 100,000 persons)and Income (median annual income per capita,in dollars).His estimated regression equation was Crime = 428 + 0.050 Income.We can conclude that:

A standardized residual ei = -2.205 indicates:

For a regression with 200 observations,we expect that about 10 residuals will exceed two standard errors.

In a sample of size n = 23,a sample correlation of r = .400 provides sufficient evidence to conclude that the population correlation coefficient exceeds zero in a right-tailed test at:

A news network stated that a study had found a positive correlation between the number of children a worker has and his or her earnings last year.You may conclude that:

In a simple regression,if the coefficient for X is positive and significantly different from zero,then an increase in X is associated with an increase in the mean (i.e. ,the expected value)of Y.

Confidence intervals for predicted Y are less precise when the residuals are very small.

A negative value for the correlation coefficient (r)implies a negative value for the slope (b1).

Two-tailed t-tests are often used because any predictor that differs significantly from zero in a two-tailed test will also be significantly greater than zero or less than zero in a one-tailed test at the same α.

The coefficient of determination is the percentage of the total variation in the response variable Y that is explained by the predictor X.

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

In least-squares regression,the residuals e₁,e₂,... ,e_n will always have a zero mean.

The critical value for a two-tailed test of H₀: β₁ = 0 at α = .05 in a simple regression with 22 observations is:

If SSR is 1800 and SSE is 200,then R² is .90.

A standardized residual e_i = -2.205 indicates:

A negative value for the correlation coefficient (r)implies a negative value for the slope (b₁).