Question 1

The regression equation for predicting X from Y is the same as the regression equation for predicting Y from X.

Accepted Answer

The regression equation for predicting X from Y is not the same as the regression equation for predicting Y from X because the slope and intercept terms are calculated based on the direction of prediction, which affects the line of best fit differently in each case.

Question 2

In the behavioral sciences where complex behaviors are studied,correlations in the .20 to .30 range (and the -.20 to -.30 range)are usually considered to be unimportant.

Accepted Answer

Correlations in the .20 to .30 range (and the -.20 to -.30 range) are generally considered weak to moderate, and can still offer important insights depending on the context and variables being studied.

Question 3

A correlation of .50 always represents a large correlation.

Accepted Answer

A correlation of .50 represents a moderate correlation, not necessarily a large one. The strength of a correlation coefficient is often dependent on the field or context in which it is being analyzed.

Question 4

It is possible for two variables to be related to one another,but for no causal relationship to exist between them.

Accepted Answer

This is possible because correlation does not necessarily imply causation. Two variables may be related to one another due to chance, coincidence, or a third factor influencing both variables.

Question 5

The absolute magnitude of the standard error of the estimate is not meaningful.

Accepted Answer

The absolute magnitude of the standard error of the estimate is meaningful as it represents the average distance between the estimated values and the actual values in a regression model. It is an important measure of the accuracy of the regression model.

Question 6

The fact that two variables are correlated necessarily implies that one variable causes the other to vary as it does.

Accepted Answer

Correlation does not necessarily imply causation. It simply means that there is a relationship between the two variables, but it may not necessarily be a causal relationship. There could be other factors at play that are causing both variables to change in a similar manner.

Question 7

When there is no linear relationship between X and Y,the z scores on X will bear no consistent relationship to the z scores on Y,either in size or sign.

Accepted Answer

When there is no linear relationship between X and Y, the z scores on X and Y will not have a consistent relationship because there is no correlation between the two variables.

Question 8

A sum of squares indicates the extent to which two sets of scores vary from one another,or covary.

Accepted Answer

A sum of squares measures the total variability within a single set of scores, not the extent to which two sets of scores vary from one another, which is measured by covariance.

Question 9

Pearson correlation will detect linear and nonlinear relationships.

Accepted Answer

Pearson correlation specifically measures the strength and direction of a linear relationship between two variables.

Question 10

When the correlation between two variables is nonzero,the value of the sum of z score products is influenced not only by the size of the correlation,but also by the sample size (N).

Accepted Answer

The sum of z score products is calculated as the sum of the products of each z score pair (from the two variables being correlated). When the correlation is nonzero, the size of the correlation will affect the magnitude of the z score products, but the sample size will also affect the sum because it determines the number of z score pairs that are being added together. Therefore, the correct statement is that the sum of z score products is influenced by both the correlation and the sample size.

Question 11

The standard error of estimate represents an average error across individuals in predicting scores on Y from the regression equation.

Accepted Answer

The standard error of estimate represents the average deviation of actual Y scores from predicted Y scores for a given value of X.

Question 12

If X helps to predict Y,then the standard error of estimate will be smaller than the standard deviation of Y.

Accepted Answer

This is because the standard error of estimate takes into account the relationship between X and Y, while the standard deviation of Y is simply a measure of the variability of Y alone. When X is included in the prediction model, it can account for some of the variability in Y, leading to a smaller standard error of estimate.

Question 13

When two variables,X and Y,are correlated,three possible reasons for their correlation are that (1)X might cause Y, (2)Y might cause X,or (3)some additional variable(s)might cause both X and Y.

Accepted Answer

This statement is true. When two variables are correlated, it is important to consider all possible explanations for the correlation, including causation and the influence of additional variables.

Question 14

The criterion for deriving the values of the slope and intercept is formally known as the least squares criterion.

Accepted Answer

The least squares criterion is a mathematical method used to determine the best fit line for a set of data. It aims to minimize the sum of the squares of the residuals (the difference between the observed values and the predicted values) by adjusting the slope and intercept of the line.

Question 15

Correlations for the types of variables typically studied by behavioral scientists will seldom exceed -.40 or +.40 and will often be considerably smaller.

Accepted Answer

Correlations in behavioral science studies are often small, with values rarely exceeding -.40 or +.40.

Question 16

The correlation that has been found between the amount of violence watched on television and aggressive behavior in children proves that watching violent television programs causes aggressive behavior.

Accepted Answer

Correlation does not imply causation. The observed correlation between watching violence on television and aggressive behavior in children does not prove that one causes the other; there could be other factors involved or a different causal relationship.

Question 17

From a statistical perspective,the designation of one variable as the X variable and one variable as the Y variable is arbitrary.

Accepted Answer

The designation of one variable as X and the other as Y does not make any difference in the statistical analysis, as long as the relationship between the variables is correctly interpreted. Therefore, it is arbitrary which variable is assigned as the independent (X) and dependent (Y) variable.

Question 18

In a regression equation,the slope and intercept are defined so as to maximize the squared vertical distances that the data points,considered collectively,are from the regression line.

Accepted Answer

The slope and intercept are defined so as to minimize the sum of squared vertical distances that the data points are from the regression line, not maximize it. This is known as the method of least squares.

Question 19

When two variables are not perfectly correlated,the statistical technique of regression can be used to identify a line that will fit the data points perfectly.

Accepted Answer

Regression is used to identify a line that best fits the data points, but it does not guarantee a perfect fit if the variables are not perfectly correlated. The line may have some degree of error involved.

Question 20

The formula for computing the intercept is a = bX.

Accepted Answer

The formula for computing the intercept is actually y = mx + b, where b is the y-intercept and m is the slope. The formula a = bX is not used for finding intercepts.

Quiz 5: Pearson Correlation and Regression: Descriptive Aspects