Question 1

_____ is a statistical technique that uses information about the relationship between an independent or predictor variable and a dependent variable to make predictions.

Accepted Answer

Bivariate regression analysis uses information about the relationship between an independent or predictor variable and a dependent variable to make predictions. Non-parametric hypothesis coefficient, covariation, and beta coefficient analysis are not techniques used for making predictions in the same way as bivariate regression analysis. Multiple regression analysis involves analyzing the relationship between multiple independent variables and a dependent variable, whereas bivariate regression analysis only involves analyzing the relationship between two variables.

Question 2

Which of the following is true of the fundamentals of regression analysis?

Accepted Answer

The use of ordinary least squares is a fundamental aspect of regression analysis that guarantees the best fitting line. The other choices are incorrect or incomplete.

Question 3

While studying the relationship between advertising and sales growth, a researcher determines that the relationship is sometimes weak and at other times moderate. This variation from one situation to another is the variation in the _____ of the relationship between advertising and sales growth.

Accepted Answer

The strength of association refers to the degree of relationship between two variables. In this case, the researcher has determined that sometimes the relationship between advertising and sales growth is weak and at other times moderate, indicating a variation in the strength of association. The other options (presence, type, direction, and dispersion) do not accurately describe this variation in the relationship.

Question 4

Which of the following is true of relationships between variables?

Accepted Answer

A linear relationship is simpler to work with because it has a constant rate of change and can be easily represented by a straight line on a graph. In contrast, a curvilinear relationship has a changing rate of change and cannot be easily represented by a straight line.

Answer: C
 A negative relationship exists between two variables when low levels of one variable are associated with high levels of another. A positive relationship, on the other hand, exists when high levels of one variable are associated with high levels of another.

Answer: E
 In a linear relationship between two variables, the strength and direction of the relationship remains constant over the range of both variables, with a constant rate of change represented by a straight line on a graph. If the strength or direction of the relationship changes over the range of the variables, it is not a linear relationship. The larger the size of the correlation coefficient between two variables, the stronger the association between them.

Question 5

Which of the following statements is true of model F statistics?

Accepted Answer

F statistics are used to test the overall significance of a regression model. A larger F statistic indicates that the regression model has more explained variance than error variance, meaning that the model is a better fit for the data. Choice B is incorrect because the relationship between the dependent and independent variables is shown by the beta coefficients. Choice C is unclear and incorrect as it does not have any logical explanation. Choice D is incorrect because multiple regression analysis is a separate concept, not a result of using F statistics. Choice E is incorrect as standardization using beta coefficients is used to compare the relative impact of different independent variables, not to augment the effects of using different scales of measurement.

Question 6

The Spearman rank order correlation coefficient differs from the Pearson correlation coefficient in that the Spearman rank order correlation:

Accepted Answer

The Spearman rank order correlation coefficient is used when variables have been measured using ordinal scales, whereas the Pearson correlation coefficient is used when variables have been measured using ratio scales.

Question 7

In bivariate regression analysis, the procedure used to determine the best-fitting line is called the:

Accepted Answer

The procedure used to determine the best-fitting line in bivariate regression analysis is called the least squares procedure. This method calculates the line of best fit by minimizing the sum of the squared residuals, or differences between the predicted values and actual values.

Question 8

The coefficient of determination:

Accepted Answer

The coefficient of determination ranges from .00 to 1.0 and represents the proportion of variation in the dependent variable that is explained by the independent variable.

Question 9

In a certain town, when the number of automobiles owned went up, the number of service stations for automobiles also went up. This illustrates the concept of _____.

Accepted Answer

The concept being illustrated is the idea that the two variables, the number of automobiles owned and the number of service stations, are changing together or "covarying". As one goes up, the other also goes up, indicating a positive correlation between the two variables.

Question 10

If a researcher is interested in measuring the effect of two independent variables on a dependent variable, he/she should use:

Accepted Answer

Multiple regression analysis allows for the examination of the effect of two or more independent variables on a dependent variable.

Question 11

The statistical procedure that produces predictions with the lowest sum of squared differences between actual and predicted values in a regression equation is called:

Accepted Answer

The statistical procedure that produces predictions with the lowest sum of squared differences between actual and predicted values in a regression equation is called ordinary least squares (OLS).

Question 12

In calculating the Pearson correlation coefficient, we assume that:

Accepted Answer

The Pearson correlation coefficient is used to measure the linear relationship between two interval- or ratio-scaled variables. Therefore, option D is the correct choice. Option A and E are incorrect because the strength and significance of a correlation coefficient do not provide information about the shape of the relationship between the two variables. Option B is incorrect because the Pearson correlation coefficient only measures the strength and direction of a linear relationship, not a curvilinear one. Option C is incorrect because the population distribution of the variables is not relevant to calculating the Pearson correlation coefficient.

Question 13

If a consistent and systematic relationship is not present between two variables, then:

Accepted Answer

If there is no consistent and systematic relationship between two variables, it means that there is no relationship at all. Therefore, the best choice is D - there is no relationship.

Question 14

Which of the following is true of a beta coefficient?

Accepted Answer

The beta coefficient shows the amount of change in the dependent variable for each unit change in the independent variable. Therefore, option E is the correct answer. Option A is incorrect as the range of beta coefficient depends on the context and is not limited to 1.00 to 3.00. Option B is partially correct as the beta coefficient is an estimated regression coefficient, not correlation coefficient. Option C is incorrect as the beta coefficient is not an F-ratio. Option D is incorrect as a positive beta means that as the size of an independent variable increases, the size of the dependent variable increases, not decreases.

Question 15

With regard to the least squares procedure, any data point that does not fall on the regression line is the result of:

Accepted Answer

Any data point that does not fall on the regression line is considered unexplained variance because it represents the variation in the dependent variable that cannot be accounted for by the independent variable(s) in the regression model.

Question 16

A _____ relationship is one between two variables whereby the strength and/or direction of the relationship changes over the range of both variables.

Accepted Answer

A curvilinear relationship is one where the strength and direction of the relationship changes over the range of both variables. This means that as the values of one variable increase, the relationship between that variable and the other variable may become stronger or weaker, or even change direction completely. A linear relationship, on the other hand, is one where the relationship between the variables is constant and does not change over the range of the variables.

Question 17

A fundamental basis of regression analysis is the assumption of:

Accepted Answer

The fundamental basis of regression analysis is to identify a straight line relationship between the independent and dependent variables. The other options are either incorrect or irrelevant to the assumptions of regression analysis.

Question 18

Which of the following statements is true of the correlation analysis?

Accepted Answer

The null hypothesis for the Pearson correlation coefficient states that the correlation coefficient is zero, which means that there is no linear association between the two variables. The Pearson correlation coefficient measures the degree of linear association between two variables that ranges from -1.0 to 1.0. The absolute value of the correlation coefficient indicates the strength of the association: the larger the absolute value, the stronger the association. Therefore, statement D is true. Statements A, B, C, and E are incorrect.

Question 19

A researcher plots a scatter diagram of two variables. The dots on the plot are scattered roughly in a circle. This indicates that the relationship (covariation) between the two variables is:

Accepted Answer

The fact that the dots are scattered roughly in a circle suggests that there is no clear relationship or trend between the two variables. Therefore, the covariation between the two variables is very close to zero.

Question 20

If the coefficient of correlation between two variables is -0.6, the coefficient of determination will be:

Accepted Answer

The coefficient of determination (r^2) is equal to the square of the coefficient of correlation (r). Therefore, in this case, r^2 = (-0.6)^2 = 0.36. So the correct answer is C) 0.36.

Quiz 12: Examining Relationships in Quantitative Research