Question 1

r² is formally known as the coefficient of indetermination.

Accepted Answer

The term "r²" is not commonly used in any field or context, and has no known meaning as a technical or mathematical term. Therefore, it cannot be said to refer to the coefficient of indetermination, and the statement is false.

Question 2

We can test the null hypothesis that ñ = 0 by transforming the sample correlation
coefficient into a statistic that has a sampling distribution that closely approximates the F
distribution with k - 1 degrees of freedom.

Accepted Answer

The sample correlation coefficient is typically transformed into a t-statistic, not an F-statistic, to test the null hypothesis that the population correlation coefficient (ρ) is zero. The t-distribution is used for this test, not the F-distribution.

Question 3

The estimated standard error of estimate estimates the average error that will be made
across individuals when predicting scores on X from the regression equation.

Accepted Answer

The estimated standard error of estimate measures the average error in predicting scores on the dependent variable (Y), not the independent variable (X), from the regression equation.

Question 4

The assumption that the population distributions of X and Y are such that their joint
distribution (that is,their scatterplot)represents a bivariate normal distribution implies
that the distribution of Y scores at any value of X is normal in the population.

Accepted Answer

If the joint distribution of X and Y is bivariate normal, it means that the marginal distribution of Y at any fixed value of X is also normal. This property is a defining characteristic of bivariate normality.

Question 5

Another useful index of the strength of the effect of one variable on another is the
intercept.

Accepted Answer

The intercept is not an index of the strength of the effect of one variable on another. It is simply the value of the dependent variable when the independent variable is equal to zero.

Question 6

Variance homogeneity can be problematic for the t test of the correlation coefficient,
especially if one is going to pursue estimation of the population regression equation.

Accepted Answer

Variance homogeneity, or homoscedasticity, is an assumption of the t-test and regression analysis. It is not problematic; rather, its violation (heteroscedasticity) can lead to issues in estimating the population regression equation.

Question 7

r² represent the proportion of variability that is shared by the two variables.

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).

Question 8

The test of the null hypothesis that ñ = 0 is based on the assumption that the variability of Y scores in the population is the same at each value of X.

Accepted Answer

The assumption of equal variance is a key assumption of many statistical tests, including the t-test and ANOVA. If this assumption is violated, it can lead to incorrect conclusions about the significance of the relationship between variables.

Question 9

A regression equation can be used to identify the value of Y that is predicted to be paired
with an individual's score on X.

Accepted Answer

A regression equation is used to predict the value of Y based on an individual's score on X, so it can be used to identify the value of Y that is predicted to be paired with an individual's score on X.

Question 10

Because the calculation of t depends only on the value of r,it is impossible to determine
values of r that will lead to a rejection of the null hypothesis that ñ = 0,given a certain
sample size.

Accepted Answer

This statement is false. The calculation of t also depends on the sample size and the degrees of freedom, in addition to the value of r. Based on the calculated t-value and the degrees of freedom, it is possible to determine the corresponding probability or p-value of obtaining a t-value as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is smaller than the predetermined significance level, the null hypothesis can be rejected. Therefore, it is possible to determine values of r that will lead to a rejection of the null hypothesis, given a certain sample size, significance level, and degrees of freedom.

Question 11

The variable being predicted,Y,is formally known as the dependent or criterion variable.

Accepted Answer

This is true, the dependent variable being predicted is formally known as the dependent or criterion variable.

Question 12

If X helps to predict Y,then the estimated standard error of estimate will be larger than the estimated standard deviation of Y,and the better the predictor X is,the larger the
estimated standard error of estimate will be.

Accepted Answer

If X helps to predict Y, the estimated standard error of estimate will be smaller than the estimated standard deviation of Y, and the better the predictor X is, the smaller the estimated standard error of estimate will be.

Question 13

The sample statistic,b,is a biased estimate of â.

Accepted Answer

The sample statistic, b, is an unbiased estimate of the population parameter, β, under the assumption that the model is correctly specified and the errors are random and normally distributed.

Question 14

The slope indicates the number of units Y is predicted to change given a one unit change in X.

Accepted Answer

This is a correct definition of what the slope represents in a linear regression model.

Question 15

The variable from which predictions are made,X,is formally known as the independent or predictor variable.

Accepted Answer

The independent or predictor variable is the variable that is manipulated or controlled to determine its effect on the dependent variable, or the variable being predicted.

Question 16

The use of the slope as an index of effect size only makes sense when the correlation
between Y and X is relatively low.

Accepted Answer

The use of the slope as an index of effect size makes sense regardless of the correlation between Y and X. The slope represents the amount of change in Y for a one-unit increase in X, regardless of the strength of the relationship between the two variables. However, when the correlation between Y and X is close to +/- 1, interpreting the slope alone may not provide a complete understanding of the relationship between the variables.

Question 17

The nature of the relationship between two correlated variables is determined through
examination of the sign of the correlation coefficient observed in the sample.

Accepted Answer

The sign of the correlation coefficient indicates the direction of the relationship between two variables. A positive sign indicates a positive relationship, while a negative sign indicates a negative relationship. Therefore, the statement is true.

Question 18

Under certain conditions,the t test for the Pearson correlation is robust with respect to violations of normality and homogeneity of variance.

Accepted Answer

The t test for Pearson correltation is robust under certain assumptions such as the sample size is sufficiently large and the data is not heavily skewed or have extreme outliers. Therefore, it is often used in practice even if the normality and homogeneity of variance assumptions are not fully met. However, if the sample size is small or there are significant deviations from the assumptions, alternative nonparametric tests may be more appropriate.

Question 19

In the context of regression,prediction merely refers to the fact that we are making
inferences about one variable from a second variable and does not imply that the latter
variable causes the former.

Accepted Answer

Regression is a statistical method used to analyze the relationship between two or more variables. It helps us to understand how the changes in one variable are associated with changes in the other variable. However, correlation does not necessarily imply causation. Therefore, making predictions using regression only means that we are using the information available to estimate the values of one variable based on the values of another variable, without implying that one variable is causing the other.

Question 20

An important weakness of regression is that prediction procedures cannot be applied to
individuals who were not included in the original data set.

Accepted Answer

Regression models can be used to make predictions for new individuals not in the original dataset, as long as the new data is within the scope of the model's variables and assumptions.

Quiz 13: Pearson Correlation and Regression: Inferential Aspects

r2 is formally known as the coefficient of indetermination.

We can test the null hypothesis that ñ = 0 by transforming the sample correlation coefficient into a statistic that has a sampling distribution that closely approximates the F distribution with k - 1 degrees of freedom.

The estimated standard error of estimate estimates the average error that will be made across individuals when predicting scores on X from the regression equation.

The assumption that the population distributions of X and Y are such that their joint distribution (that is,their scatterplot)represents a bivariate normal distribution implies that the distribution of Y scores at any value of X is normal in the population.

Another useful index of the strength of the effect of one variable on another is the intercept.

Variance homogeneity can be problematic for the t test of the correlation coefficient, especially if one is going to pursue estimation of the population regression equation.

r2 represent the proportion of variability that is shared by the two variables.

The test of the null hypothesis that ñ = 0 is based on the assumption that the variability of Y scores in the population is the same at each value of X.

A regression equation can be used to identify the value of Y that is predicted to be paired with an individual's score on X.

Because the calculation of t depends only on the value of r,it is impossible to determine values of r that will lead to a rejection of the null hypothesis that ñ = 0,given a certain sample size.

The variable being predicted,Y,is formally known as the dependent or criterion variable.

If X helps to predict Y,then the estimated standard error of estimate will be larger than the estimated standard deviation of Y,and the better the predictor X is,the larger the estimated standard error of estimate will be.

The sample statistic,b,is a biased estimate of â.

The slope indicates the number of units Y is predicted to change given a one unit change in X.

The variable from which predictions are made,X,is formally known as the independent or predictor variable.

The use of the slope as an index of effect size only makes sense when the correlation between Y and X is relatively low.

The nature of the relationship between two correlated variables is determined through examination of the sign of the correlation coefficient observed in the sample.

Under certain conditions,the t test for the Pearson correlation is robust with respect to violations of normality and homogeneity of variance.

In the context of regression,prediction merely refers to the fact that we are making inferences about one variable from a second variable and does not imply that the latter variable causes the former.

An important weakness of regression is that prediction procedures cannot be applied to individuals who were not included in the original data set.

r² is formally known as the coefficient of indetermination.

r² represent the proportion of variability that is shared by the two variables.