Question 1

When there is no relationship between variables, ______.
A) the scatterplot is inaccurate
B) an accurate prediction of the mean of the other variable can be made
C) a calculation error has been made
D) no accurate prediction can be made

Accepted Answer

The answer of When there is no relationship between variables,...

Question 2

The R measures the relationship between two or more predictor variables and a criterion variable.

Accepted Answer

The R, specifically the Pearson correlation coefficient, measures the strength and direction of the linear relationship between two continuous variables. It is commonly used in regression analysis to examine the relationship between predictor variables and a criterion variable (which is also a continuous variable).

Question 3

Multiple correlation is defined as the mathematical equation that predicts a score on a criterion variable from scores on two or more predictor variables.

Accepted Answer

The answer of Multiple correlation is defined as the mathematical...

Question 4

The linear regression equation represents ______.
A) the value of X
B) the value of Y
C) the "best fit" relationship between two variables
D) a horizontal relationship

Accepted Answer

The linear regression equation represents the "best fit" relationship between two variables. It shows the mathematical formula or model that best predicts the values of the dependent variable (Y) based on the values of the independent variable (X). The equation is used to make predictions or to understand the relationship between the variables. Therefore, option C is the best choice.

Question 5

The R is also known as the regression coefficient

Accepted Answer

The R in statistics typically refers to the correlation coefficient, not the regression coefficient. The regression coefficient is usually denoted by beta (β) in regression analysis.

Question 6

A correlation matrix is ______.
A) a table of Pearson correlations between variables
B) a scatterplot display
C) a representation of the linear regression equation
D) the point of the Y-intercept

Accepted Answer

A correlation matrix is a table that shows the Pearson correlation coefficient between every pair of variables in a dataset. It is a common tool for exploring the relationships between variables and identifying potential patterns or trends. Unlike scatterplots, which visualize the relationship between two variables, a correlation matrix allows for a quick overview of the entire dataset's correlations. It is not a representation of the linear regression equation or the Y-intercept point.

Question 7

Including multiple predictors in one analysis ______.
A) guarantees significant results
B) is less accurate than using only one predictor 
C) offers no real research advantage
D) should increase the amount of explained variance in the criterion

Accepted Answer

Including multiple predictors in one analysis should increase the amount of explained variance in the criterion. However, it does not guarantee significant results and can actually lead to less accurate results if the predictors are not related to the criterion variable. Additionally, using multiple predictors allows for the examination of the unique contribution of each predictor to the criterion variable, offering a significant research advantage.

Question 8

Correlation involves measuring the relationship between variables.

Accepted Answer

Correlation is a statistical technique used to measure the relationship between two or more variables.

Question 9

Multiple correlation is defined as a family of statistical procedures assessing the relationship between two or more predictor variables and a criterion variable.

Accepted Answer

The definition given is correct and describes multiple correlation.

Question 10

Developing a linear regression equation requires calculating the slope (b) and ______.
A) the X intercept
B) the value of t
C) the value of m
D) the Y-intercept (a)

Accepted Answer

To develop a linear regression equation, we need to determine the slope (b) and the Y-intercept (a). The equation takes the form Y = a + bX, where X is the independent variable, Y is the dependent variable, a is the Y-intercept, and b is the slope. Therefore, the correct option is D, the Y-intercept.

Question 11

Correlation involves the prediction of a criterion variable while regression involves measuring the relationship between variables.

Accepted Answer

Correlation measures the strength and direction of the relationship between two variables, while regression involves predicting the value of a dependent variable based on the value(s) of one or more independent variables.

Question 12

Multiple correlation provides researchers the ability to ______.
A) test a variety of effects
B) accurately support the alternative hypothesis
C) provide assurance of significant results
D) easily calculate results

Accepted Answer

Multiple correlation allows researchers to test the relationship between multiple independent variables and a dependent variable, providing the ability to examine a variety of effects simultaneously. It does not necessarily guarantee accurate support for the alternative hypothesis or significant results, but it does provide a more comprehensive understanding of the relationships between variables. It may not be considered easy to calculate by some researchers.

Question 13

When a relationship is found between variables, an opportunity exists to ______.
A) predict one variable from another
B) reject the null hypothesis
C) reject the alternative hypothesis
D) prove the validity of the research

Accepted Answer

When a relationship is found between variables, it means that changes in one variable can lead to changes in the other variable. Therefore, it is possible to use this relationship to predict the value of one variable from the value of the other variable, which is the essence of regression analysis. The other options are not necessarily true. Rejecting the null hypothesis or accepting the alternative hypothesis depends on the p-value and the level of significance. Proving the validity of the research is a challenging task, and finding a correlation does not necessarily mean that the research is valid.

Question 14

The multiple regression equation may be reported once the ______.
A) regression coefficients have been calculated
B) Y-intercept has been calculated
C) slope has been determined
D) regression coefficient and the Y-intercept have been calculated

Accepted Answer

The multiple regression equation includes both the regression coefficients (slopes) and the Y-intercept, so both must be calculated before the equation can be reported.

Question 15

Regression involves the prediction of a criterion variable.

Accepted Answer

Regression is a statistical technique used to predict or estimate the value of a criterion (or dependent) variable based on one or more predictor (or independent) variables. Therefore, it involves the prediction of a criterion variable.

Question 16

The F-ratio is used to test the significance by transforming R.

Accepted Answer

The F-ratio is used to test the significance of the difference between two variances. It is calculated by dividing the variance of the first sample by the variance of the second sample. If the F-ratio is greater than 1, then the difference between the two variances is considered to be significant.

Question 17

In the regression equation: Y′ = 3.66 + .15(X). Y′ refers to the Y-intercept.

Accepted Answer

Y′ refers to the predicted value of Y for a given value of X, not the Y-intercept. The Y-intercept is represented by the constant coefficient in the regression equation (in this case, 3.66).

Question 18

Multiple correlation measures the combined relationship of all the predictors with the criterion.

Accepted Answer

Multiple correlation measures the relationship between a criterion variable and multiple predictor variables, taking into account their combined effects.

Question 19

A multiple correlation R is significant when it is statically ______.
A) equal to 1.0
B) different from .00
C) equal to .01
D) different from 1.0

Accepted Answer

A multiple correlation R is significant when it is different from .00, indicating that there is a relationship between the variables being studied. A correlation of 1.0 indicates a perfect positive relationship, while a correlation of -1.0 indicates a perfect negative relationship. A correlation of .01 is a very weak correlation, and a correlation of 1.0 or -1.0 cannot be a multiple correlation as it can only exist between two variables, not multiple variables. Therefore, the best choice is B, different from .00.

Question 20

The value for the slope of the regression equation is ______.
A) always a positive number
B) always a negative number
C) either positive or negative
D) a squared result

Accepted Answer

The slope of the regression equation can be either positive or negative, depending on the direction of the relationship between the two variables. If there is a positive relationship, the slope will be positive, and if there is a negative relationship, the slope will be negative. Therefore, the slope can be either positive or negative.

Quiz 14: Linear Regression and Multiple Correlation

When there is no relationship between variables, ______.

The R measures the relationship between two or more predictor variables and a criterion variable.

Multiple correlation is defined as the mathematical equation that predicts a score on a criterion variable from scores on two or more predictor variables.

The linear regression equation represents ______.

The R is also known as the regression coefficient

A correlation matrix is ______.

Including multiple predictors in one analysis ______.

Correlation involves measuring the relationship between variables.

Multiple correlation is defined as a family of statistical procedures assessing the relationship between two or more predictor variables and a criterion variable.

Developing a linear regression equation requires calculating the slope (b) and ______.

Correlation involves the prediction of a criterion variable while regression involves measuring the relationship between variables.

Multiple correlation provides researchers the ability to ______.

When a relationship is found between variables, an opportunity exists to ______.

The multiple regression equation may be reported once the ______.

Regression involves the prediction of a criterion variable.

The F-ratio is used to test the significance by transforming R.

In the regression equation: Y′ = 3.66 + .15(X). Y′ refers to the Y-intercept.

Multiple correlation measures the combined relationship of all the predictors with the criterion.

A multiple correlation R is significant when it is statically ______.

The value for the slope of the regression equation is ______.