ECO 391 Final Exam | Latest study set |
Questions and verified Answers
(T/F) The correlation coefficient can only range between 0 and 1. - ANSW-False - The correlation can
range between -1 and 1
(T/F) The value 0.75 of a sample correlation coefficient indicates a stronger linear relationship than that
of 0.60. - ANSW-True - As the absolute value of the sample correlation coefficient increases, the linear
relationship between x and y becomes stronger.
(T/F) The value -0.75 of a sample correlation coefficient indicates a stronger linear relationship than that
of 0.60. - ANSW-True - As the absolute value of the sample correlation coefficient approaches 1, the
linear relationship between x and y becomes stronger.
(T/F) In testing the population correlation coefficient, the alternative hypothesis is HA: ρxy does not
equal 1 - ANSW-False - Testing the population correlation coefficient involves a test to determine if this
coefficient is different from 0.
(T/F) Another name for an explanatory variable is the dependent variable. - ANSW-False - Explanatory
variable is also called independent variable.
(T/F) In the simple linear regression model, β0 is the y-intercept of the line E(y) = β0 + β1x - ANSW-True -
In the simple linear regression model, β0 is the intercept, and β1 is the slope.
The correlation coefficient r = -0.85 could indicate a:
A. Very weak positive linear relationship.
B. Very strong negative linear relationship.
C. Very weak negative linear relationship.
D. Very strong positive linear relationship. - ANSW-B. Very strong negative linear relationship
Which of the following statements is least accurate concerning correlation analysis?
A. Correlation does not imply causation.
B. The correlation coefficient captures only a linear relationship.
C. The correlation coefficient may not be a reliable measure when outliers are present in one or the both
of the variables.
D. The correlation coefficient describes both the direction and strength of the relationship between two
variables only if the two variables have the same unitsof measurement. - ANSW-D. The correlation
coefficient describes both the direction and strength of the relationship between two variables only if
the two variables have the same unitsof measurement.
The sample standard deviations for x and y are 10 and 15, respectively. The covariance between x and y
is -30. The correlation coefficient between x and y is:
A. -0.2
B. -0.5
C. 0.5
D. 0.2 - ANSW-A. -0.2
A regression equation was estimated as y hat = −100 + 0.5x1. If x1= 20, the predicted value of y is:
A. -80
, B. -90
C. 110
D. 120 - ANSW-B. -90
Consider the following simple linear regression model: y = β0 + β1x + ε, the response variable is:
A. y
B. x
C. ε
D. β0 - ANSW-A. y
Consider the following data: x bar = 20, y bar = −5, sx = 2, sy = 4, and b1 = 0.4. What is the linear
regression equation?
A. y = −13 − 0.4x
B. y = −13 + 0.4x
C. y = 3 − 0.4x
D. y = 3 − 0.4x - ANSW-B. y = −13 + 0.4x
(T/F) If two linear regression models have the same number of explanatory variables, a model with an R2
value of 0.45 is a better prediction model than a model with an R2 value of 0.65. - ANSW-False
(T/F) A model with an R2 value of 0.65 is always a better prediction model than a model with an R2 value
of 0.6. - ANSW-False - We need to compare the adjusted R2. It could be that the model with a lower R2
actually has a higher adjusted R2.
Simple linear regression analysis differs from multiple regression analysis in that:
A. Simple linear regression uses only one explanatory variable.
B. The coefficient of correlation is meaningless in simple linear regression.
C. Goodness-of-fit measures cannot be calculated with simple linear regression.
D. The coefficient of determination is always higher in simple linear regression. - ANSW-A. Simple linear
regression uses only one explanatory variable.
In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, what is the
standard error of the estimate?
A. -1
B. 0
C. +1
D. Infinity - ANSW-B. 0
The standard error of the estimate measures:
A. the variability of the explanatory variables.
B. the variability of the values of the sample regression coefficients.
C. the variability of the observed y-values around the predicted y-values.
D. the variability of the predicted y-values around the mean of the observed y-values. - ANSW-C. the
variability of the observed y-values around the predicted y-values.
Questions and verified Answers
(T/F) The correlation coefficient can only range between 0 and 1. - ANSW-False - The correlation can
range between -1 and 1
(T/F) The value 0.75 of a sample correlation coefficient indicates a stronger linear relationship than that
of 0.60. - ANSW-True - As the absolute value of the sample correlation coefficient increases, the linear
relationship between x and y becomes stronger.
(T/F) The value -0.75 of a sample correlation coefficient indicates a stronger linear relationship than that
of 0.60. - ANSW-True - As the absolute value of the sample correlation coefficient approaches 1, the
linear relationship between x and y becomes stronger.
(T/F) In testing the population correlation coefficient, the alternative hypothesis is HA: ρxy does not
equal 1 - ANSW-False - Testing the population correlation coefficient involves a test to determine if this
coefficient is different from 0.
(T/F) Another name for an explanatory variable is the dependent variable. - ANSW-False - Explanatory
variable is also called independent variable.
(T/F) In the simple linear regression model, β0 is the y-intercept of the line E(y) = β0 + β1x - ANSW-True -
In the simple linear regression model, β0 is the intercept, and β1 is the slope.
The correlation coefficient r = -0.85 could indicate a:
A. Very weak positive linear relationship.
B. Very strong negative linear relationship.
C. Very weak negative linear relationship.
D. Very strong positive linear relationship. - ANSW-B. Very strong negative linear relationship
Which of the following statements is least accurate concerning correlation analysis?
A. Correlation does not imply causation.
B. The correlation coefficient captures only a linear relationship.
C. The correlation coefficient may not be a reliable measure when outliers are present in one or the both
of the variables.
D. The correlation coefficient describes both the direction and strength of the relationship between two
variables only if the two variables have the same unitsof measurement. - ANSW-D. The correlation
coefficient describes both the direction and strength of the relationship between two variables only if
the two variables have the same unitsof measurement.
The sample standard deviations for x and y are 10 and 15, respectively. The covariance between x and y
is -30. The correlation coefficient between x and y is:
A. -0.2
B. -0.5
C. 0.5
D. 0.2 - ANSW-A. -0.2
A regression equation was estimated as y hat = −100 + 0.5x1. If x1= 20, the predicted value of y is:
A. -80
, B. -90
C. 110
D. 120 - ANSW-B. -90
Consider the following simple linear regression model: y = β0 + β1x + ε, the response variable is:
A. y
B. x
C. ε
D. β0 - ANSW-A. y
Consider the following data: x bar = 20, y bar = −5, sx = 2, sy = 4, and b1 = 0.4. What is the linear
regression equation?
A. y = −13 − 0.4x
B. y = −13 + 0.4x
C. y = 3 − 0.4x
D. y = 3 − 0.4x - ANSW-B. y = −13 + 0.4x
(T/F) If two linear regression models have the same number of explanatory variables, a model with an R2
value of 0.45 is a better prediction model than a model with an R2 value of 0.65. - ANSW-False
(T/F) A model with an R2 value of 0.65 is always a better prediction model than a model with an R2 value
of 0.6. - ANSW-False - We need to compare the adjusted R2. It could be that the model with a lower R2
actually has a higher adjusted R2.
Simple linear regression analysis differs from multiple regression analysis in that:
A. Simple linear regression uses only one explanatory variable.
B. The coefficient of correlation is meaningless in simple linear regression.
C. Goodness-of-fit measures cannot be calculated with simple linear regression.
D. The coefficient of determination is always higher in simple linear regression. - ANSW-A. Simple linear
regression uses only one explanatory variable.
In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, what is the
standard error of the estimate?
A. -1
B. 0
C. +1
D. Infinity - ANSW-B. 0
The standard error of the estimate measures:
A. the variability of the explanatory variables.
B. the variability of the values of the sample regression coefficients.
C. the variability of the observed y-values around the predicted y-values.
D. the variability of the predicted y-values around the mean of the observed y-values. - ANSW-C. the
variability of the observed y-values around the predicted y-values.
