Question 1

If the Pearson correlation for a set of scores is equal to +1.00,then the Spearman correlation for the same scores would also be equal to +1.00.

Accepted Answer

The statement is true. A Pearson correlation of +1.00 indicates a perfect positive linear relationship between two variables. The Spearman correlation measures the strength and direction of the monotonic relationship between two variables, and a perfect positive monotonic relationship also results in a Spearman correlation of +1.00.

Question 2

It is possible for the regression equation to have none of the actual (observed)data points located on the regression line.

Accepted Answer

The regression line is a statistical summary of the relationship between two variables based on the available data. It is possible for the regression line to be a close approximation of the actual data points, but it is not guaranteed that all data points will fall on the line. In fact, it is common for some data points to deviate from the line due to measurement error or other factors.

Question 3

The line defined by the Y = -3X + 6 slopes up to the right.

Accepted Answer

The slope of the line is -3, which means it slopes down to the right.

Question 4

A sample of n = 25 pairs of scores (X and Y values)produces a correlation of r = -0.40.Are these sample data sufficient to conclude that there is a significant non-zero correlation between X and Y in the population? Use a two-tailed test at the .05 level of significance.

Accepted Answer

The answer of A sample of n = 25 pairs...

Question 5

If people are classified by age (over 30/under 30)and by political affiliation (Democrat/Republican),then the point-biserial correlation would be the proper technique to measure the relationship between the two variables.

Accepted Answer

Point-biserial correlation is used to measure the relationship between a continuous variable and a binary variable, not between two binary variables. In this case, both variables are binary (over 30/under 30 and Democrat/Republican), so point-biserial correlation is not appropriate. A chi-square test or phi coefficient would be more appropriate in measuring the relationship between these two variables.

Question 6

The line produced by the equation Y = 4X - 5 crosses the vertical axis at Y = 5.

Accepted Answer

The line crosses the vertical axis at Y = -5, not Y = 5.

Question 7

The phi-coefficient is used to measure relationships for data that would also be appropriate for an independent-measures t test.

Accepted Answer

The phi-coefficient is used to measure relationships between two categorical variables, while an independent-measures t test is used to compare mean differences between two groups on a continuous variable. Therefore, the phi-coefficient would not be appropriate for data that is appropriate for an independent-measures t test.

Question 8

The F-ratio evaluating the significance of a linear regression equation based on n = 10 pairs of X and Y scores has df = 1,9.

Accepted Answer

The answer of The F-ratio evaluating the significance of a...

Question 9

The phi-coefficient is the correct correlation to use when both X and Y are dichotomous variables.

Accepted Answer

The phi-coefficient is specifically designed to measure the correlation between two dichotomous variables, making it the correct choice when both X and Y are dichotomous. Other correlation coefficients, such as Pearson's r or Spearman's rho, are better suited for continuous or ordinal data.

Question 10

The sign of the correlation (+/)is generally meaningless for the point-biserial correlation and the phi-coefficient.

Accepted Answer

The sign of the correlation is typically not interpreted for these two types of correlation coefficients, as they do not have a directional association like Pearson's correlation coefficient.

Question 11

For linear regression,the value of SS_residual can be computed directly by Σ(Y - ?4Y)².

Accepted Answer

The correct formula for computing the sum of squared residuals (SSR) in linear regression is Σ(Y - Ŷ)², where Ŷ is the predicted value of Y based on the regression line. _residual is not a recognized term in linear regression. Therefore, the statement in the question is false.

Question 12

A set of X and Y scores has M_X = 4,M_Y = 10,SS_X = 10,and SP = 5.The regression equation for these scores is Y = 0.5X  8.

Accepted Answer

The statement is false. The value of SP (standard error of estimate) cannot be determined from the given information.

Question 13

If the Pearson correlation between X and Y is r = 0.60,then the regression equation predicts 36% of the variance in the Y scores.

Accepted Answer

The coefficient of determination (r squared) is equal to the square of the correlation coefficient (r) which in this case is (0.6)^2 = 0.36. This means that the regression equation can predict 36% of the variance in the Y scores.

Question 14

For a regression equation with a positive slope,if the X value is above the mean for the X scores,then the predicted Y value will be above the mean for the Y scores.

Accepted Answer

If the regression equation has a positive slope, it means that as X increases, Y is also expected to increase. If an X value is above the mean for the X scores, it indicates a higher-than-average value, and according to the positive slope, the predicted Y value will also be higher than the mean for the Y scores.

Question 15

If other factors are held constant,if the Pearson correlation between X and Y is r = 0.80,then the regression equation will produce more accurate predictions than would be obtained if r = 0.60.

Accepted Answer

A higher correlation coefficient (r) indicates a stronger linear relationship between X and Y, which means that using the regression equation to predict Y based on X will be more accurate when r is higher (i.e. 0.80) than when r is lower (i.e. 0.60).

Question 16

A set of X and Y scores has SS_X = 10,SS_Y = 36,and SP = 20.The regression equation for these scores will have a slope constant of 2.

Accepted Answer

Since the slope constant is not given by any of the SSS or SP variables, it can be assumed to be a constant value. Therefore, it is possible for the regression equation to have a slope constant of 2.

Question 17

If the Spearman correlation for a set of scores is equal to +1.00,then the Pearson correlation for the same scores would also be equal to +1.00.

Accepted Answer

The answer of If the Spearman correlation for a set...

Question 18

For a regression equation with a slope of b = 3,if M_X = 3 and M_Y = 10,then the Y-intercept for the equation is 1.

Accepted Answer

The answer of For a regression equation with a slope...

Quiz 14: Correlation and Regression