Question 1

One would predict that the sons of a large group of the tallest pro basketball players will have a mean height somewhat less than that of their fathers.This can be explained by the phenomenon of

Accepted Answer

Regression is the phenomenon where extreme values tend to move towards the mean in subsequent generations, also known as regression towards the mean. Since the tall pro basketball players are extreme values in terms of height, their sons are likely to have a mean height closer to the overall average, resulting in regression towards the mean.

Question 2

As the level of significance increases (e.g., from .01 to .05) in a test of the null hypothesis, the critical value of the Pearson's r

Accepted Answer

As the level of significance increases, the critical region becomes larger, making it easier to reject the null hypothesis. This means the absolute value of the critical value of Pearson's r decreases, as it requires a smaller correlation to be considered statistically significant.

Question 3

The best prediction using a multiple regression equation will occur when each predictor has a correlation with the other independent variables, and a correlation with the dependent variable.

Accepted Answer

The best prediction in multiple regression occurs when each predictor has a low correlation with other independent variables (to avoid multicollinearity) and a high correlation with the dependent variable (to ensure each predictor contributes significantly to explaining the variance in the dependent variable).

Question 4

A study found that college students who work part-time have higher GPAs than either students who don't work at all or students who have full-time jobs.This finding indicates that the relationship between weekly hours worked and GPA is

Accepted Answer

The relationship is curvilinear because the GPA increases with part-time work compared to no work or full-time work, indicating a non-linear relationship where the effect of hours worked on GPA changes direction across different levels of work commitment.

Question 5

If the correlation between X and Y is .70, the proportion of variance in Y that is predictable from X is

Accepted Answer

The coefficient of determination (r squared) is equal to the square of the correlation coefficient (r). Therefore, r squared = 0.70 squared = 0.49. This means that 49% of the variance in Y is predictable from X.

Question 6

The correlation between SAT and GPA would be lowest for which one of the following populations?

Accepted Answer

The correlation between SAT and GPA may be less relevant for seniors who have won the Westinghouse Talent Search because they may have already distinguished themselves in other ways that are not measured by standardized tests such as the SAT. This may result in a weaker correlation between SAT scores and GPA for this population compared to the general population of high school seniors.

Question 7

For n = 1,000 the computed r between X and Y is r = .45.If n were increased to 4,000 from the same population, the r would probably be

Accepted Answer

The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. It is not affected by the sample size, assuming the samples are from the same population and the relationship between variables remains constant. Increasing the sample size from 1,000 to 4,000 would not change the value of r, assuming the additional data is consistent with the relationship observed in the initial sample.

Question 8

Which of the following is most likely to be statistically significant

Accepted Answer

A larger sample size increases the probability of finding statistically significant results, while a higher correlation indicates a stronger relationship between variables, making it more likely to achieve statistical significance.

Question 9

The standard error of estimate, s_e, is the standard deviation of

Accepted Answer

The standard error of estimate (s) represents the average distance of observed data points from the regression line. It is the standard deviation of the errors or residuals, which are the differences between the actual Y scores and the predicted Y scores. Therefore, the correct choice is C. The other options (A, B, and D) do not describe the standard error of estimate correctly.

Question 10

Exhibit 13-7: Choose the index of correlation appropriate for use in each of the following.
Exhibit
-Refer to Exhibit 13-7.Teachers ranking of importance of educational outcomes and their pupils ranking of these outcomes

Accepted Answer

Spearman rho is appropriate for use when the data is ordinal, which is the case for the rankings of educational outcomes by both teachers and pupils. Pearson's r is appropriate for use when the data is continuous and normally distributed, which is not the case here. The Phi coefficient is appropriate for use with nominal data, which is also not the case here. Therefore, the best choice for this data is Spearman rho.

Question 11

The purpose of canonical correlation is to determine the magnitude of the relationship between

Accepted Answer

Canonical correlation is used to determine the relationship between two sets of variables. In this case, it is used to determine the magnitude of the relationship between a set of predictor variables and a set of criterion variables.

Question 12

A correlation of -.65 between test anxiety and college GPA means that

Accepted Answer

A correlation of -.65 indicates a moderate to strong negative correlation between test anxiety and college GPA. This means that there is a tendency for students with high test anxiety to receive lower grades than students with low test anxiety. It does not necessarily mean that test anxiety causes low grades or that low grades contribute to high test anxiety.

Question 13

If a computed Pearson's correlation coefficient is statistically significant at the .01 level,

Accepted Answer

A statistically significant Pearson's correlation coefficient at the 0.01 level indicates that the probability of the correlation occurring by chance is less than 1%. This suggests that there is a high likelihood that a relationship exists between the two variables, but it does not guarantee an important or strong relationship, nor does it indicate the direction of the relationship (positive or negative).

Question 14

A general aptitude test correlates .45 with success in a particular college.To improve the predictive accuracy, the students are also given three other aptitude measures, all of which correlate very highly with one another and with the first test.What will be the likely effect of adding the scores from the three additional tests to the regression equation?

Accepted Answer

The three additional tests are highly correlated with the general aptitude test, which means that they are already measuring much of the same variance in determining college success. Adding them to the regression equation may slightly increase the predictive accuracy, but only to a small extent. There is no indication that the addition of these tests will significantly improve or decrease predictive accuracy, so option B is the best choice.

Question 15

In testing the hypothesis that the correlation parameter is zero, the critical value of r decreases as sample size

Accepted Answer

As the sample size increases, the sample correlation becomes more reliable and the standard error of the estimate decreases. Therefore, a smaller correlation coefficient is needed to reject the null hypothesis of zero correlation. This leads to a decrease in the critical value of r as the sample size increases.

Question 16

A scattergram is helpful because it illustrates the

Accepted Answer

A scattergram can illustrate the magnitude and direction of a relationship between two variables as well as the presence of a nonlinear relationship. Therefore, all of these options are true.

Question 17

The correlation between variables X and Y was found to be .95.This indicates that

Accepted Answer

A correlation of .95 indicates a strong positive relationship, meaning that as scores on X increase, scores on Y also tend to increase, and vice versa.

Question 18

Exhibit 13-7: Choose the index of correlation appropriate for use in each of the following.
Exhibit
-Refer to Exhibit 13-7.Final exam scores in algebra and scores on a math aptitude test

Accepted Answer

Pearson's r is the appropriate choice for examining the correlation between two continuous variables, which is the case for final exam scores in algebra and scores on a math aptitude test.

Question 19

Exhibit 13-7: Choose the index of correlation appropriate for use in each of the following.
Exhibit
-Refer to Exhibit 13-7.Success or failure in algebra and gender

Accepted Answer

The Phi coefficient is the most appropriate index of correlation for this scenario as it examines the relationship between two dichotomous variables (success or failure in algebra and gender).

Question 20

If one wanted to determine the degree of variability of the actual Y scores about the predicted Y scores, the appropriate statistic is

Accepted Answer

The standard error of estimate is a measure of the degree of variability of the actual Y scores about the predicted Y scores. It measures the average distance that the observed values fall from the regression line. The other options, such as the standard deviation of the predicted Y scores or the standard deviation of the predictor scores, do not provide a direct measure of the degree of variability of the actual Y scores about the predicted Y scores.

Quiz 13: Correlation Research