Question 1

When the errors in a regression model are not independent, the regression model is said to have autocorrelation.

Accepted Answer

A) True 
 B)False  True

Question 2

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 percentage 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 percentage of the variation in Y explained by X. 
D) It is calculated using sums of squares (e.g., SSR, SSE, SST). B

Question 3

If n = 15 and r = .4296, the corresponding t statistic to test for zero correlation is:

Accepted Answer

A) 1.715. 
B) 7.862. 
C) 2.048. 
D) impossible to determine without α. 
A) 1.715. 
B) 7.862. 
C) 2.048. 
D) impossible to determine without α. A

Question 4

In a sample of n = 36, the critical value of the correlation coefficient for a two-tailed test at α = .05 is:

Accepted Answer

A) ±.329 
B) ±.387 
C) ±.423 
D) ±.497 
A) ±.329 
B) ±.387 
C) ±.423 
D) ±.497

Question 5

Find the sample correlation coefficient for the following data. $$\begin{array} { | c | c | } 
\hline X & Y \
\hline 3 & 8 \
\hline 7 & 12 \
\hline 5 & 13 \
\hline 9 & 10 \
\hline 11 & 17 \
\hline 13 & 23 \
\hline 15 & 35 \
\hline 17 & 34 \
\hline
\end{array}$$

Accepted Answer

A) .8911 
B) .9124 
C) .9822 
D) .9556 
A) .8911 
B) .9124 
C) .9822 
D) .9556

Question 6

The least squares regression line gives unbiased estimates of β0 and β1.

Accepted Answer

A) True 
 B)False

Question 7

A researcher's regression results are shown below using n = 8 observations. $$\begin{array} { l r r } 
\hline \text { Variable } & \text { Coefficient } & \text { Standard Error } \
\hline \text { Intercept } & - 0.1667 & 2.8912 \
\text { Slope } & 1.8333 & 0.2307 \
\hline
\end{array}$$ The 95 percent confidence interval for the slope is:

Accepted Answer

A) [1.333, 2.284]. 
B) [1.602, 2.064]. 
C) [1.268, 2.398]. 
D) [1.118, 2.449]. 
A) [1.333, 2.284]. 
B) [1.602, 2.064]. 
C) [1.268, 2.398]. 
D) [1.118, 2.449].

Question 8

Which statement is not correct?

Accepted Answer

A) Spurious correlation can often be reduced by expressing X and Y in per capita terms. 
B) Autocorrelation is mainly a concern when we are using time-series data. 
C) Heteroscedastic residuals will have roughly the same variance for any value of X. 
D) Standardized residuals make it easy to identify outliers or instances of poor fit. 
A) Spurious correlation can often be reduced by expressing X and Y in per capita terms. 
B) Autocorrelation is mainly a concern when we are using time-series data. 
C) Heteroscedastic residuals will have roughly the same variance for any value of X. 
D) Standardized residuals make it easy to identify outliers or instances of poor fit.

Question 9

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 10

In a simple bivariate regression with 25 observations, which statement is most nearly correct?

Accepted Answer

A) A nonstandardized residual whose value is ei = 4.22 would be considered an outlier. 
B) A leverage statistic of 0.16 or more would indicate high leverage. 
C) Standardizing the residuals will eliminate any heteroscedasticity. 
D) Non-normal residuals imply biased coefficient estimates, a major problem. 
A) A nonstandardized residual whose value is ei = 4.22 would be considered an outlier. 
B) A leverage statistic of 0.16 or more would indicate high leverage. 
C) Standardizing the residuals will eliminate any heteroscedasticity. 
D) Non-normal residuals imply biased coefficient estimates, a major problem.

Question 11

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

Accepted Answer

A) True 
 B)False

Question 12

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 13

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 14

Bob thinks there is something wrong with Excel's fitted regression. What do you say?

Accepted Answer

A) The estimated equation is obviously incorrect. 
B) The R2 looks a little high but otherwise it looks OK. 
C) Bob needs to increase his sample size to decide. 
D) The relationship is linear, so the equation is credible. 
A) The estimated equation is obviously incorrect. 
B) The R2 looks a little high but otherwise it looks OK. 
C) Bob needs to increase his sample size to decide. 
D) The relationship is linear, so the equation is credible.

Question 15

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 16

A standardized residual equal to -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 17

In a simple regression, the correlation coefficient r is the square root of R2.

Accepted Answer

A) True 
 B)False

Question 18

A researcher's results are shown below using Femlab (labor force participation rate among females) to try to predict Cancer (death rate per 100,000 population due to cancer) in the 50 U.S. states. $$\begin{array} { l r } 
\hline { \text { Regression Statistics } } \
\hline \text { Multiple R } & 0.313422848 \
\text { R Square } & 0.098233882 \
\text { Adjusted R Square } & 0.079447088 \
\text { Standard Error } & 32.07003698 \
\text { Observations } & 50 \
\hline
\end{array}$$ $$\begin{array} { l c r r } 
\hline \text { Variable } & \text { Coefficients } & \text { Standard Error } &  { t \text { Stat } } \
\hline \text { Intercept } & 343.619889 & 61.0823514 & 5.62552 \
\text { Femlab } & - 2.2833659 & 0.99855319 & - 2.28667 \
\hline
\end{array}$$ Which statement is valid regarding the relationship between Femlab and Cancer?

Accepted Answer

A) A rise in female labor participation rate will cause the cancer rate to decrease within a state. 
B) This model explains about 10 percent of the variation in state cancer rates. 
C) At the .05 level of significance, there isn't enough evidence to say the two variables are related. 
D) If your sister starts working, the cancer rate in your state will decline. 
A) A rise in female labor participation rate will cause the cancer rate to decrease within a state. 
B) This model explains about 10 percent of the variation in state cancer rates. 
C) At the .05 level of significance, there isn't enough evidence to say the two variables are related. 
D) If your sister starts working, the cancer rate in your state will decline.

Question 19

In linear regression between two variables, a significant relationship exists when the p-value of the t test statistic for the slope is greater than α.

Accepted Answer

A) True 
 B)False

Question 20

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.

When the errors in a regression model are not independent, the regression model is said to have autocorrelation.

Which is not true of the coefficient of determination?

If n = 15 and r = .4296, the corresponding t statistic to test for zero correlation is:

In a sample of n = 36, the critical value of the correlation coefficient for a two-tailed test at α = .05 is:

Find the sample correlation coefficient for the following data. X Y 3 8 7 12 5 13 9 10 11 17 13 23 15 35 17 34

The least squares regression line gives unbiased estimates of β₀ and β₁.

A researcher's regression results are shown below using n = 8 observations. Variable Coefficient Standard Error Intercept -0.1667 2.8912 Slope 1.8333 0.2307 The 95 percent confidence interval for the slope is:

Which statement is not correct?

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 a simple bivariate regression with 25 observations, which statement is most nearly correct?

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

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

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?

Bob thinks there is something wrong with Excel's fitted regression. What do you say?

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

A standardized residual equal to -2.205 indicates:

In a simple regression, the correlation coefficient r is the square root of R².

In linear regression between two variables, a significant relationship exists when the p-value of the t test statistic for the slope is greater than α.

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:

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 the errors in a regression model are not independent, the regression model is said to have autocorrelation.

Which is not true of the coefficient of determination?

If n = 15 and r = .4296, the corresponding t statistic to test for zero correlation is:

In a sample of n = 36, the critical value of the correlation coefficient for a two-tailed test at α = .05 is:

Find the sample correlation coefficient for the following data. X Y 3 8 7 12 5 13 9 10 11 17 13 23 15 35 17 34

The least squares regression line gives unbiased estimates of β0 and β1.

A researcher's regression results are shown below using n = 8 observations. Variable Coefficient Standard Error Intercept -0.1667 2.8912 Slope 1.8333 0.2307 The 95 percent confidence interval for the slope is:

Which statement is not correct?

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 a simple bivariate regression with 25 observations, which statement is most nearly correct?

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

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

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?

Bob thinks there is something wrong with Excel's fitted regression. What do you say?

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

A standardized residual equal to -2.205 indicates:

In a simple regression, the correlation coefficient r is the square root of R2.

In linear regression between two variables, a significant relationship exists when the p-value of the t test statistic for the slope is greater than α.

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:

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 least squares regression line gives unbiased estimates of β₀ and β₁.

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?

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

In a simple regression, the correlation coefficient r is the square root of R².