Question 1

A negative correlation between two variables X and Y usually yields a negative p-value for r.

Accepted Answer

A) True 
 B)False

Question 2

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 3

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 + 0.0214 Distance. If Distance increases by 50 miles, the expected Time would increase by:

Accepted Answer

A) 1.07 days 
B) 7.13 days 
C) 2.14 days 
D) 1.73 days 
A) 1.07 days 
B) 7.13 days 
C) 2.14 days 
D) 1.73 days

Question 4

If the attendance at a baseball game is to be predicted by the equation Attendance = 16,500 - 75 Temperature, what would be the predicted attendance if Temperature is 90 degrees?

Accepted Answer

A) 6,750 
B) 9,750 
C) 12,250 
D) 10,020 
A) 6,750 
B) 9,750 
C) 12,250 
D) 10,020

Question 5

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

Accepted Answer

A) True 
 B)False

Question 6

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 + 0.0214 Distance, based on a sample of 20 shipments. The estimated standard error of the slope is 0.0053. Find the value of tcalc to test for zero slope.

Accepted Answer

A) 2.46 
B) 5.02 
C) 4.04 
D) 3.15 $b _ { 1 } / s _ { b }$ 
A) 2.46 
B) 5.02 
C) 4.04 
D) 3.15 $b _ { 1 } / s _ { b }$

Question 7

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

Accepted Answer

A) True 
 B)False

Question 8

A fitted regression Profit = -570 + 30 Sales (all variables in thousands of dollars) was estimated from a random sample of 20 pharmacies. For a pharmacy with Sales = 10, we predict that Profit will be:

Accepted Answer

A) 3570. 
B) 2430. 
C) -270. 
D) 870. 
A) 3570. 
B) 2430. 
C) -270. 
D) 870.

Question 9

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

Accepted Answer

A) True 
 B)False

Question 10

If the residuals from a fitted regression violate the assumption of homoscedasticity, we know that:

Accepted Answer

A) they are normally distributed. 
B) they are independent of one another. 
C) their variance is not constant. 
D) there are extreme outliers. 
A) they are normally distributed. 
B) they are independent of one another. 
C) their variance is not constant. 
D) there are extreme outliers.

Question 11

If you have a strong outlier in the residuals, it may represent a different causal system.

Accepted Answer

A) True 
 B)False

Question 12

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

Question 13

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 14

Studentized (or standardized) residuals permit us to detect cases where the regression predicts poorly.

Accepted Answer

A) True 
 B)False

Question 15

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 16

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

Accepted Answer

A) True 
 B)False

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

The ordinary least squares regression line always passes through the point $( \bar { x } , \bar { y } )$

Accepted Answer

A) True 
 B)False

Question 19

Mary noticed that old coins are smoother and more worn. She weighed 31 nickels and recorded their ages, and then performed a simple regression to estimate the model Weight = β0 + β1 Age, where weight is the weight of the coin in grams and Age is the age of the coin in years. Her results are shown below. Write a brief analysis of these results, using what you have learned in this chapter. Make a prediction of Weight when Age = 10 and also when Age = 20. What does this tell you? Is the intercept meaningful in this regression?
Regression Analysis
$$\begin{array} { c c r l } 
r ^ { 2 } & 0.442 & n & 31 \
r & - 0.665 & k & 1 \
\text { or } & 0.050 & \text { Dep. Var. Weight (gm) }
\end{array}$$

ANOVA table
$\begin{array}{rcccrr}
\hline \text { Source } & \text { SS } & \text { df } & M S & F & p \text {-value } \
\hline \text { Regression } & 0.0582 & 1 & 0.0582 & 22.99 & 4.48 \mathrm{E}-05 \
\text { Residual } & 0.0734 & 29 & 0.0025 & & \
\hline \text { Total } & 0.1316 & 30 & &
\end{array}$

Regression output  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;  &emsp;   confidence interval
$\begin{array}{crrrrrr}
\hline \text { variables } & \text { coefficients } & \text { std. emor } & f(d f=29) & \text { p-value } & 95 \% \text { lower } & 95 \% \text { upper } \
\hline \text { Intercept } & 5.0210 & 0.0137 & 367.740 & 9.33 \mathrm{E}-55 & 4.9931 & 5.0489 \
\text { Age (Yrs) } & -0.0040 & 0.0008 & -4.795 & 4.48 \mathrm{E}-05 & -0.0057 & -0.0023 \
\hline
\end{array}$

Accepted Answer

It is reasonable to postulate a causal r

Question 20

When homoscedasticity exists, we expect that a plot of the residuals versus the fitted Y:

Accepted Answer

A) will form approximately a straight line. 
B) crosses the centerline too many times. 
C) will yield a Durbin-Watson statistic near 2. 
D) will show no pattern at all. 
A) will form approximately a straight line. 
B) crosses the centerline too many times. 
C) will yield a Durbin-Watson statistic near 2. 
D) will show no pattern at all.

A negative correlation between two variables X and Y usually yields a negative p-value for r.

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

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 + 0.0214 Distance. If Distance increases by 50 miles, the expected Time would increase by:

If the attendance at a baseball game is to be predicted by the equation Attendance = 16,500 - 75 Temperature, what would be the predicted attendance if Temperature is 90 degrees?

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

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

A fitted regression Profit = -570 + 30 Sales (all variables in thousands of dollars) was estimated from a random sample of 20 pharmacies. For a pharmacy with Sales = 10, we predict that Profit will be:

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

If the residuals from a fitted regression violate the assumption of homoscedasticity, we know that:

If you have a strong outlier in the residuals, it may represent a different causal system.

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

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:

Studentized (or standardized) residuals permit us to detect cases where the regression predicts poorly.

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.

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

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

The ordinary least squares regression line always passes through the point $( \bar { x } , \bar { y } )$

When homoscedasticity exists, we expect that a plot of the residuals versus the fitted Y:

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

A negative correlation between two variables X and Y usually yields a negative p-value for r.

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

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 + 0.0214 Distance. If Distance increases by 50 miles, the expected Time would increase by:

If the attendance at a baseball game is to be predicted by the equation Attendance = 16,500 - 75 Temperature, what would be the predicted attendance if Temperature is 90 degrees?

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

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

A fitted regression Profit = -570 + 30 Sales (all variables in thousands of dollars) was estimated from a random sample of 20 pharmacies. For a pharmacy with Sales = 10, we predict that Profit will be:

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

If the residuals from a fitted regression violate the assumption of homoscedasticity, we know that:

If you have a strong outlier in the residuals, it may represent a different causal system.

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

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:

Studentized (or standardized) residuals permit us to detect cases where the regression predicts poorly.

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.

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

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

The ordinary least squares regression line always passes through the point (xˉ,yˉ)( \bar { x } , \bar { y } )(xˉ,yˉ​)

When homoscedasticity exists, we expect that a plot of the residuals versus the fitted Y:

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

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

The ordinary least squares regression line always passes through the point $( \bar { x } , \bar { y } )$