Question 1

Positive correlations are also described as indirect, whereas negative correlations are also described as direct.

Accepted Answer

This statement is incorrect. Positive correlations are also described as direct, meaning that as one variable increases, the other variable also increases. Negative correlations are described as indirect, meaning that as one variable increases, the other variable decreases.

Question 2

in a positive correlation, as the value of X increases, the value of Y also increases

Accepted Answer

This is the definition of a positive correlation.

Question 3

The strength of a correlation depends on whether it's positive or negative

Accepted Answer

The strength of a correlation is independent of its direction, whether it's positive or negative. The strength of the correlation is determined by the closeness of the relationship between the two variables and is measured by the correlation coefficient.

Question 4

A correlation of .78 is stronger than a correlation of -.92.

Accepted Answer

A correlation of -0.92 indicates a strong negative relationship, while a correlation of 0.78 represents a strong positive relationship. However, the strength of the correlation coefficient does not depend on whether it is positive or negative. Therefore, a correlation of -0.92 is stronger than a correlation of 0.78.

Question 5

When testing a correlation, the null hypothesis states that there is no correlation

Accepted Answer

The null hypothesis of a correlation states that there is no significant relationship between the two variables being tested.

Question 6

A least squares regression line minimizes the distance from each datum in the dataset to it.

Accepted Answer

The least squares regression line is defined as the line that minimizes the sum of the squared distances between the line and each datum in the dataset, therefore it does minimize the distance from each datum to it.

Question 7

In a regression equation, if b is positive, then the correlation between the predictor and outcome must be negatively correlated.

Accepted Answer

This statement is false. If b is positive, it means that there is a positive relationship between the predictor and outcome variables, not a negative correlation.

Question 8

In a regression equation, a stronger equation between the two variables would lead to more horizontal regression line.

Accepted Answer

A stronger relationship between two variables in a regression equation would lead to a steeper regression line, not a more horizontal one, as it indicates a greater change in the dependent variable for a given change in the independent variable.

Question 9

In a regression equation, if a is negative, then the correlation between the predictor and outcome must be negatively correlated.

Accepted Answer

A negative intercept (a) in a regression equation does not determine the direction of the correlation between the predictor and outcome. The correlation is determined by the slope (b) of the regression line.

Question 10

The coefficient of determination is used to explain the proportion of variance shared between two variables

Accepted Answer

The coefficient of determination, also known as R-squared, measures how well the regression line fits the data and explains the proportion of variance in the dependent variable that is explained by the independent variable. It ranges from 0 to 1, with 1 meaning that all of the variance in the dependent variable is explained by the independent variable. Therefore, the statement is true.

Question 11

A strong negative correlation will lead to a large positive coefficient of determination

Accepted Answer

The coefficient of determination, denoted as R^2, measures the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It is the square of the correlation coefficient (r). Whether the correlation is positive or negative, squaring it will result in a positive value, indicating the strength of the relationship, not the direction. A strong negative correlation will result in a high R^2 value, indicating a large proportion of variance in the dependent variable is explained by the independent variable.

Question 12

Smaller coefficients of determination means that the two variables have a weaker relationship

Accepted Answer

A smaller coefficient of determination indicates that there is less variation in the dependent variable that is explained by the independent variable, which suggests a weaker relationship between the two variables.

Question 13

A correlation of .04 and -.04 will have the same coefficient of determination.

Accepted Answer

The coefficient of determination is equal to the square of the correlation coefficient. In both cases, the square of 0.04 (0.04 x 0.04 = 0.0016) and the square of -0.04 (-0.04 x -0.04 = 0.0016) are equal to 0.0016. Therefore, both correlations will have the same coefficient of determination.

Question 14

Correlation might not mean causation, but if data is analyzed by an ANOVA or t-test, a significant result is a causal relationship.

Accepted Answer

A significant result from an ANOVA or t-test indicates only that there is a statistically significant difference between two or more groups, but it does not necessarily imply a causal relationship. Other factors, such as confounding variables or chance, could also be responsible for the observed difference. Therefore, additional research and analysis are needed to establish causality.

Question 15

Correlations measures dependence between two variables

Accepted Answer

Correlations measure the strength and direction of the relationship between two variables.

Question 16

If a correlation between two variables is -.2, the coefficient of determination is -.04

Accepted Answer

The coefficient of determination is the squared value of the correlation coefficient, so in this case it would be .04, not -.04.

Question 17

When testing a correlation between 2 variables with 20 pairs of data, the degrees of freedom is 19

Accepted Answer

In correlation analysis, the degrees of freedom (df) is calculated as n - 2, where n is the number of pairs. So, for 20 pairs of data, df = 20 - 2 = 18.

Question 18

In regression, the y-variable is often the predicted variable. The x-variable is used to predict the y-variable.

Accepted Answer

This is true. In regression, the aim is to find a relationship between the predictor variable (x-variable) and the response variable (y-variable), where the x-variable is used to predict the y-variable.

Question 19

The regression coefficient is negatively correlated with the correlation coefficient of the same two variables

Accepted Answer

The regression coefficient and the correlation coefficient of the same two variables are not inherently negatively correlated. The sign of the regression coefficient indicates the direction of the relationship between the variables, similar to the correlation coefficient. Both can be positive or negative, indicating the direction of the relationship, but one does not determine the negativity or positivity of the other.

Question 20

The Pearson correlation can be applied to linear relationships as well as curvilinear relationships

Accepted Answer

The Pearson correlation coefficient measures the strength and direction of a linear relationship between two variables, but it is not suitable for assessing curvilinear relationships.

Quiz 13: Correlation and Regression: Are We Related