Question 1

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

Accepted Answer

The slope of the line defined by the equation Y = -3X + 6 is -3, which means the line slopes down to the right.

Question 2

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 3

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

Accepted Answer

The regression equation is Y = bX + a. Given b = 3, MX = 3, and MY = 10, we can use the formula a = MY - bMX to find the Y-intercept: a = 10 - (3*3) = 1.

Question 4

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 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

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^2), which in this case would be 0.36 or 36%, indicating that the regression equation can explain 36% of the variance in the Y scores.

Question 7

In a test for significance of a Pearson correlation for a sample of n = 30 individuals,you determine the critical value by using df = 29.

Accepted Answer

The degrees of freedom (df) for a Pearson correlation test is calculated as n - 2, so for a sample of n = 30, df should be 28.

Question 8

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 the strength of association between two binary variables, whereas an independent-measures t-test is used to compare the means of two groups on a continuous variable.

Question 9

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

Accepted Answer

The slope constant of a regression equation can be calculated as: 
b = SP / SSₓ
Since SSₓ = 10 and SP = 20, we can calculate the slope constant as:
b = 20 / 10
b = 2
Therefore, the statement is true.

Question 10

A set of X and Y scores has MX = 4,MY = 10,SSₓ = 10,and SP = 5.The regression equation for these scores is Y = 0.5X + 8.

Accepted Answer

The slope (b) of the regression line is calculated as SP/SSₓ, which is 5/10 = 0.5. The intercept (a) is calculated using the formula a = MY - b*MX, which gives a = 10 - 0.5*4 = 8. Therefore, the regression equation is Y = 0.5X + 8.

Question 11

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

Accepted Answer

The regression line represents the best fit line for the given set of data. It is not necessary that all the actual data points will fall exactly on this line. In fact, it is common for there to be some amount of variation or error between the actual data points and the regression line.

Question 12

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

Accepted Answer

The sign of the correlation in point-biserial correlation and phi-coefficient is determined by the direction of the relationship between the two variables, which is already represented by the correlation coefficient. Therefore, the sign itself does not provide any additional information and is considered meaningless.

Question 13

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

Accepted Answer

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

Question 14

For linear regression,the value of SSᵣₑsᵢdᵤₐl can be computed directly by Σ(Y -Ŷ)².

Accepted Answer

SSᵣₑsᵢdᵤₐl represents the sum of square of residuals or errors in the linear regression model. Residuals are the difference between the actual observed values (Y) and the predicted values (Ŷ) by the linear regression model. Therefore, the direct formula to calculate SSᵣₑsᵢdᵤₐl is Σ(Y -Ŷ)².

Question 15

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

A positive slope indicates a positive relationship between X and Y variables. If the X value is above the mean, it suggests that the X variable has a higher value than the average value of X. As the regression equation predicts the value of Y based on the given value of X, a higher X value will result in a higher predicted Y value. Therefore, the predicted Y value will be above the mean for the Y scores.

Question 16

If other factors are held constant and 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 relationship between X and Y, which means that the regression equation will be able to predict Y values more accurately based on X values. Therefore, if r = 0.80, the predictions will be more accurate than if r = 0.60 (which indicates a weaker relationship between X and Y).

Question 17

For a two-tailed hypothesis test evaluating the significance of a correlation,the null hypothesis states that the sample correlation is zero.

Accepted Answer

The answer of For a two-tailed hypothesis test evaluating the...

Question 18

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

This is true. If the Pearson correlation is equal to +1.00, it means that there is a perfect positive relationship between the two variables. The Spearman correlation measures the strength of monotonic association between two variables, and if there is a perfect positive relationship, then the ranks of the scores will also be perfectly correlated. Therefore, the Spearman correlation would also be equal to +1.00.

Question 19

Assuming that other factors are constant,a correlation of r = -0.95 will result in more accurate predictions than a correlation of r = +0.70.

Accepted Answer

A correlation coefficient of -0.95 indicates a strong negative relationship between the variables, meaning that as one variable increases, the other decreases with high predictability. Therefore, this correlation coefficient would result in more accurate predictions. On the other hand, a correlation coefficient of +0.70 indicates a moderate positive relationship between the variables, meaning that as one variable increases, the other also increases, but with less predictability. Therefore, this correlation coefficient would result in less accurate predictions.

Question 20

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

Accepted Answer

The line produced by the equation Y = 4X - 5 crosses the vertical axis at Y = -5, not Y = 5.

Quiz 14: Correlation and Regression.

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

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.

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

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.

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.

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.

In a test for significance of a Pearson correlation for a sample of n = 30 individuals,you determine the critical value by using df = 29.

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

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

A set of X and Y scores has MX = 4,MY = 10,SSₓ = 10,and SP = 5.The regression equation for these scores is Y = 0.5X + 8.

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

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

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

For linear regression,the value of SSᵣₑsᵢdᵤₐl can be computed directly by Σ(Y -Ŷ)².

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.

If other factors are held constant and 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.

For a two-tailed hypothesis test evaluating the significance of a correlation,the null hypothesis states that the sample correlation is zero.

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.

Assuming that other factors are constant,a correlation of r = -0.95 will result in more accurate predictions than a correlation of r = +0.70.

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