Question 1

The formula y = a + b(x) represents the ______.
A) Pearson's r
B) regression coefficient
C) correlation coefficient
D) regression line

Accepted Answer

The formula y = a + b(x) represents the regression line, which is used in regression analysis to predict the value of one variable (y) based on the value of another variable (x). It shows the relationship between the two variables and can be used to make predictions about future values of y based on changes in x. Therefore, option D is the correct answer. The other options (Pearson's r, regression coefficient, and correlation coefficient) are all related to statistical measures of the strength and direction of a relationship between two variables but are not specifically related to the formula y = a + b(x).

Question 2

A researcher wants to estimate voter turnout for different regions of the country. She divides the country into four regions. How many dummy variables will she have in the equation?
A) 1
B) 2
C) 3
D) 4

Accepted Answer

To estimate voter turnout for different regions of the country, the researcher must create a regression equation that includes a variable for each region. However, she cannot include all four regions as variables in the equation because that would result in perfect multicollinearity (i.e., the variables would be perfectly correlated with each other). To avoid this problem, she can use one of the regions as a baseline and create dummy variables for the other three regions. This will result in three dummy variables (representing the three remaining regions) in the equation. Therefore, the best choice is C) 3.

Question 3

In the equation y = a + b(x), b stands for the ______.
A) independent variable
B) correlation coefficient
C) regression coefficient
D) dependent variable

Accepted Answer

In the equation y = a + b(x), b is the regression coefficient, representing the change in the dependent variable (y) per unit change in the independent variable (x). It is not the independent variable (A), correlation coefficient (B), or dependent variable (D) in this equation.

Question 4

In the equation y = a + b(x) which variable represents the y-intercept?
A) y
B) a
C) b
D) x

Accepted Answer

In the equation y = a + b(x), the variable a represents the y-intercept because it is the constant term added to the slope (b) times the value of x. When x is zero, the only remaining term is a, which gives the value of y at the point where the line intersects the y-axis.

Question 5

A researcher is working with two variables measured at the interval level. Which statistical tool should the researcher use? A) $\chi$² analysis B) correlation analysis C) proportion analysis D) cross-tabulation

Accepted Answer

The researcher should use correlation analysis as it is used to measure the strength and direction of the relationship between two continuous variables at the interval level. The other options (A, C, and D) are not appropriate for two interval level variables.

Question 6

A graphical display where the independent variable is measured along the horizontal axis and the dependent variable is measured along the vertical axis is called a ______.
A) bar graph
B) line graph
C) pie chart
D) scatterplot

Accepted Answer

A scatterplot is a graphical display where the independent variable is measured along the horizontal axis and the dependent variable is measured along the vertical axis.

Question 7

Multiple regression analysis produces a ______ for each independent variable in the model. A) partial regression coefficient B) partial correlation coefficient C) partial $\chi$² D) partial adjusted R-square

Accepted Answer

Multiple regression analysis produces a partial regression coefficient for each independent variable in the model, which represents the change in the dependent variable associated with a one-unit change in that independent variable while holding all other independent variables constant. The other options are not accurate descriptions of what is produced by multiple regression analysis.

Question 8

A researcher working with data about individuals' ages and their income wants to know how income is related to age. Does income go up or down or remain constant with age? Which analysis would help the researcher understand this relationship best?
A) correlation analysis
B) regression analysis
C) means comparison analysis
D) logistic regression analysis

Accepted Answer

Correlation analysis measures the strength and direction of the linear relationship between two variables. In this case, it would help the researcher determine whether income increases, decreases, or remains constant with age.

Question 9

Multiple regression is both ______ and ______.
A) linear; interactive
B) linear; additive
C) linear; regressive
D) linear; spurious

Accepted Answer

Multiple regression is a linear and additive statistical method that is used to establish relationships between a dependent variable and two or more independent variables. It assumes that the effects of independent variables on the dependent variables are independent and additive, and not interactive or regressive. Therefore, choice B is the correct answer.

Question 10

The regression coefficient is also known as the ______. A) correlation coefficient B) R² C) test value D) slope of the line

Accepted Answer

The regression coefficient is also known as the slope of the line because it represents the rate of change in the dependent variable for every unit increase in the independent variable. The other options are not synonyms for the regression coefficient.

Question 11

R² always has a value between ______. A) 1 and 2 B) -1 and 1 C) -1 and 0 D) 0 and 1

Accepted Answer

R², or the coefficient of determination, measures the proportion of variance in the dependent variable that is predictable from the independent variable(s) and ranges from 0 to 1.

Question 12

A researcher conducting a study of turnout in the fifty states finds a regression coefficient of .35. This tells the researcher that ______.
A) turnout increases by .35 for each one unit increase in the independent variable
B) turnout increases by .35 for each year a person ages
C) turnout decreases by .35 for each one unit increase in the independent variable
D) turnout increases by .35 for each one unit decrease in the independent variable

Accepted Answer

The regression coefficient of .35 indicates that for each one unit increase in the independent variable, the dependent variable (in this case, turnout) increases by .35. This is a direct interpretation of the coefficient in a linear regression model.

Question 13

A researcher is studying her students' test scores and the amount of coffee (number of cups) consumed before the exam. In the equation y = a + b(x) which variable represents the test scores?
A) y
B) a
C) b
D) x

Accepted Answer

In the equation y = a + b(x), y represents the dependent variable or the outcome variable, which in this case is the test score. Therefore, choice A is the best choice.

Question 14

A Pearson's r value of .51 signifies a ______.
A) weak negative relationship
B) weak positive relationship
C) moderate positive relationship
D) moderate negative relationship

Accepted Answer

A Pearson's r value of .51 signifies a moderate positive relationship, meaning that there is a moderate level of correlation between the two variables being measured.

Question 15

If no relationship exists between variables, Pearson's r takes on the value of ______.
A) -1
B) 0
C) +1
D) no value

Accepted Answer

When no relationship exists between variables, Pearson's r takes on the value of 0.

Question 16

In a scatterplot, the ______ variable is measured on the horizontal axis and the ______ variable is on the vertical axis.
A) dependent; independent
B) independent; dependent
C) dependent; intervening
D) control; dependent

Accepted Answer

In a scatterplot, the variable being manipulated or controlled is plotted on the horizontal axis (independent variable) and the variable being measured (dependent variable) is on the vertical axis.

Question 17

A bivariate analysis is used to analyze the relationship between a(n) ______.
A) interval-level dependent variable and any independent variable at any level
B) ordinal-level dependent variable and any independent variable at any level
C) ratio-level dependent variable and any independent variable at any level
D) nominal-level dependent variable and any independent variable at any level

Accepted Answer

Bivariate analysis can be used to analyze the relationship between an interval-level dependent variable and any independent variable at any level. It is not appropriate for nominal-level data since nominal variables cannot be ranked, and it is more difficult to calculate measures of association for ordinal and ratio-level data.

Question 18

One reason to perform multiple regression analysis is to ______ for the effects of additional independent variables.
A) eliminate
B) alleviate
C) minimize
D) control

Accepted Answer

The purpose of multiple regression analysis is to control for the effects of additional independent variables by including them in the model. This allows for a more accurate understanding of the relationship between the dependent variable and each independent variable, as it accounts for the influence of other potentially confounding factors. Eliminating, alleviating, or minimizing the effects of independent variables is not the aim of multiple regression analysis.

Question 19

The relationship between two variables is called ______.
A) association
B) affiliation
C) correlation
D) regression

Accepted Answer

The relationship between two variables is most commonly referred to as correlation. Association and affiliation are related concepts, but they are more broadly defined than just the relationship between two variables. Regression is a statistical analysis that is used to model the relationship between variables, but it is not the term used to describe the relationship itself.

Question 20

Which of the following formalizes the intuitive judgment made about the direction and strength of a relationship? A) Pearson's r B) $\chi$² C) Pearson's correlation coefficient D) regression coefficient

Accepted Answer

Pearson's correlation coefficient, also known as Pearson's r, formalizes the intuitive judgment made about the direction and strength of a relationship. It is a measure of linear correlation between two variables, ranging from -1 (perfect negative correlation) to 1 (perfect positive correlation), with 0 indicating no correlation. Option A (Pearson's r) is the same as option C. Option B appears to be a nonsensical string of characters. Option D (regression coefficient) is a measure of the effect of one independent variable on a dependent variable in a regression model, but it does not necessarily capture the overall direction and strength of the relationship between the two variables.

Quiz 8: Correlation and Linear Regression

The formula y = a + b(x) represents the ______.

A researcher wants to estimate voter turnout for different regions of the country. She divides the country into four regions. How many dummy variables will she have in the equation?

In the equation y = a + b(x) , b stands for the ______.

In the equation y = a + b(x) which variable represents the y-intercept?

A researcher is working with two variables measured at the interval level. Which statistical tool should the researcher use?

A graphical display where the independent variable is measured along the horizontal axis and the dependent variable is measured along the vertical axis is called a ______.

Multiple regression analysis produces a ______ for each independent variable in the model.

A researcher working with data about individuals' ages and their income wants to know how income is related to age. Does income go up or down or remain constant with age? Which analysis would help the researcher understand this relationship best?

Multiple regression is both and .

The regression coefficient is also known as the ______.

R² always has a value between ______.

A researcher conducting a study of turnout in the fifty states finds a regression coefficient of .35. This tells the researcher that ______.

A researcher is studying her students' test scores and the amount of coffee (number of cups) consumed before the exam. In the equation y = a + b(x) which variable represents the test scores?

A Pearson's r value of .51 signifies a ______.

If no relationship exists between variables, Pearson's r takes on the value of ______.

In a scatterplot, the variable is measured on the horizontal axis and the variable is on the vertical axis.

A bivariate analysis is used to analyze the relationship between a(n) ______.

One reason to perform multiple regression analysis is to ______ for the effects of additional independent variables.

The relationship between two variables is called ______.

Which of the following formalizes the intuitive judgment made about the direction and strength of a relationship?