Question 1

Both Pearson r and Spearman rho can range from - 1.00 to +1.00.

Accepted Answer

Both Pearson r and Spearman rho are correlation coefficients that range from -1.00 to +1.00, indicating the strength and direction of the relationship between two variables.

Question 2

If scores are z scores and if r equals 1 then zX will always equal zY .

Accepted Answer

If r equals 1, it means there is a perfect positive linear relationship between X and Y. Therefore, every score in X will have a corresponding score in Y that is the same distance from their respective means, resulting in identical z scores for each score in X and Y.

Question 3

The formula for rho is actually just the formula for Pearson's r simplified to apply to lower order scaling.

Accepted Answer

This statement is true. Pearson's r is a measure of linear correlation that applies to interval or ratio scaled variables, while rho is a measure of rank correlation that applies to ordinal or interval scaled variables. However, the formula for rho is simply the formula for Pearson's r applied to the ranks of the variables.

Question 4

The slope of a line is a measure of its rate of change.

Accepted Answer

The slope of a line indicates how much the y-coordinate changes for each unit increase in the x-coordinate. Therefore, it is a measure of the rate of change of the line.

Question 5

Since r is so widely used, it is appropriate to calculate r for nonlinear data.

Accepted Answer

The correlation coefficient r is designed for linear relationships, so it is not appropriate to use it to measure the strength or direction of nonlinear relationships.

Question 6

If one calculates r for a set of data and r equals 0.84, one can be certain that the relationship between the variables is not spurious.

Accepted Answer

While a correlation coefficient of 0.84 indicates a strong positive relationship between two variables, it does not necessarily mean that the relationship is not spurious. Spurious correlations can still occur even with high correlation coefficients if there is a confounding variable or if the relationship is coincidental.

Question 7

A correlation coefficient expresses the direction but not the magnitude of a relationship.

Accepted Answer

A correlation coefficient expresses both the direction and the magnitude of a relationship between two variables.

Question 8

In a straight line the slope approaches zero as the line comes near the point X , Y .

Accepted Answer

The slope of a straight line is constant and does not change as it approaches any particular point (X, Y).

Question 9

One reason for calculating r from z scores is to make r independent of units and scaling.

Accepted Answer

Calculating r from z scores standardizes the data, making it independent of the original units and scaling used in the data. Therefore, r becomes a unitless correlation coefficient.

Question 10

Restricting the range of either X or Y will generally lower the correlation between the variables.

Accepted Answer

Restricting the range of either X or Y means that there is less variability in one of the variables, which can lower the correlation between the variables. When the range is restricted, there may be fewer data points available to calculate the correlation coefficient, and this can lead to a weaker correlation. Additionally, if the restricted range happens to include outliers, this can further reduce the correlation between the variables.

Question 11

The coefficient of determination equals  .

Accepted Answer

The answer of The coefficient of determination equals  ....

Question 12

In a linear relationship all the points must fall on a straight line.

Accepted Answer

A linear relationship implies that the points generally follow a straight line trend, but they do not have to fall exactly on a straight line due to potential variability or noise in the data.

Question 13

If the value of rho for a set of ordinal data equaled 0.68, the value of r for the same data would be 0.68.

Accepted Answer

The value of Spearman's rho (ρ) for ordinal data does not necessarily equal the value of Pearson's r for the same data, as they measure correlation differently. Pearson's r is used for linear relationships between two continuous variables, while Spearman's rho is used for ordinal data or non-linear relationships.

Question 14

In an inverse relationship as one variable gets larger the other variable gets smaller.

Accepted Answer

In an inverse relationship, as one variable increases, the other variable decreases. So, the answer is true.

Question 15

The value of r obtained by calculating the correlation between X and Y is the same as the correlation between Y and X .

Accepted Answer

Correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. The value of r obtained by calculating the correlation between X and Y will be the same as the value of r obtained by calculating the correlation between Y and X. This is because the correlation coefficient is not affected by the order of the variables in the calculation.

Question 16

In a perfect linear relationship all the points must fall on a straight line.

Accepted Answer

In a linear relationship, all the points should fall on a straight line. If any points fall off the line, it suggests a deviation from linearity.

Question 17

The coefficient of determination equals the proportion of variability accounted for by the relationship between the variables.

Accepted Answer

This is a true statement. The coefficient of determination (r-squared) measures the proportion of variability in the response variable that is explained by the predictor variable(s). It can range from 0 to 1, where 0 means that the predictor variable(s) do not explain any variability in the response variable, and 1 means that the predictor variable(s) explain all of the variability in the response variable.

Question 18

If the value of r on ratio scaled raw data were 0.87 and the pairs of numbers were converted to ordinal data, and r calculated for the ordinal data, r would equal 0.87.

Accepted Answer

When converting ratio scaled raw data to ordinal data, the values are ranked rather than using their actual magnitudes. This process can change the relationship between the data points, potentially altering the correlation coefficient (r). Therefore, r calculated for the ordinal data may not equal 0.87, as it was for the ratio scaled raw data.

Question 19

The easiest way to determine if a relationship is linear is to calculate the regression line.

Accepted Answer

While calculating the regression line can provide information about the relationship between two variables, it does not necessarily determine if the relationship is linear. A scatter plot and examining the pattern of the data can help determine if a relationship is linear.

Question 20

The correlation between two variables when N = 2 will always be perfect.

Accepted Answer

When N = 2, there are only two data points and hence only one line can pass through them. Therefore, the correlation between the two variables will always be perfect (either +1 or -1) as there is no variation in the data.

Quiz 6: Correlation