Question 1

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 variation within a single set of scores, not the covariation between two sets of scores. Covariation is measured by covariance or correlation.

Question 2

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 true because when X helps to predict Y, it means that the relationship between X and Y is strong. This strong relationship reduces the variability in Y that cannot be explained by X, thus making the standard error of estimate smaller than the standard deviation of Y.

Question 3

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 4

The formula for computing the intercept is a = bX.

Accepted Answer

The formula for computing the intercept in a linear equation is a = Y - bX, where 'a' is the intercept, 'b' is the slope, 'X' is the mean of the independent variable, and 'Y' is the mean of the dependent variable.

Question 5

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

This is because z-scores are calculated based on the mean and standard deviation of the data. If there is no linear relationship between X and Y, then their means and standard deviations will be independent of each other, which means z-scores on X will bear no consistent relationship to the z-scores on Y.

Question 6

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 find the line that best fits the data points, but it is rare that the line will fit the data points perfectly, especially if there is noise or variability in the data. The line will generally have some error or residual associated with it.

Question 7

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 actually considered modest or moderate correlations in the behavioral sciences, and can be important depending on the context and research question being investigated.

Question 8

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 different from the regression equation for predicting Y from X because they have different dependent and independent variables, leading to different slopes and intercepts.

Question 9

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

This is true. The sum of z score products is affected by both the correlation and the sample size. As the sample size increases, the sum of z score products increases as well, even if the correlation remains the same.

Question 10

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 relationship between watching violent TV and aggressive behavior may be influenced by other factors.

Question 11

A correlation of .50 always represents a large correlation.

Accepted Answer

A correlation of .50 may represent a moderate-to-strong correlation, but it does not always indicate a large correlation. The strength of a correlation also depends on the context and the variables being measured.

Question 12

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 formal method for calculating the values of the slope and intercept in linear regression.

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. Correlation does not necessarily imply causation, and there could be other underlying factors that are causing the correlation between two variables.

Question 14

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 amount that the observed values of Y differ from the predicted values of Y, taking into account the variability within the sample data. Therefore, it can be considered as an average error in predicting scores on Y from the regression equation for the sample data.

Question 15

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 imply causation. Just because two variables are correlated, it does not necessarily mean that one is causing the other to vary. There could be other factors or variables at play that are causing both variables to vary together.

Question 16

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

This statement is true. Correlations between variables studied in behavioral science are typically modest, with values rarely exceeding +/- .40.

Question 17

Pearson correlation will detect linear and nonlinear relationships.

Accepted Answer

Pearson correlation only measures the strength and direction of linear relationships between two variables, not nonlinear relationships.

Question 18

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 which variable is the X variable and which is the Y variable is arbitrary and does not affect the statistical analysis or interpretation of the relationship between the variables.

Question 19

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 to minimize the sum of squared vertical distances, not to maximize it. This is known as the least squares criterion.

Question 20

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

Accepted Answer

Correlation does not imply causation, meaning that two variables can show a statistically significant relationship without any actual causal connection between them.

Quiz 5: Pearson Correlation and Regression: Descriptive Aspects