Question 1

An example of a joint category of two variables is the count of all non-drinkers who are also nonsmokers.

Accepted Answer

A joint category of two variables involves combining categories from each variable to examine their intersection. In this case, the combination of being a non-drinker and a non-smoker creates a joint category.

Question 2

Comparing a numerical variable across two or more subpopulations is known as a comparison problem.

Accepted Answer

A comparison problem involves analyzing how a numerical variable differs across two or more subpopulations, aiming to understand variations or similarities between these groups.

Question 3

Correlation is not useful for describing the strength and direction of nonlinear relationships.

Accepted Answer

Correlation measures the strength and direction of linear relationships between variables, and may not accurately describe nonlinear relationships.

Question 4

The correlation between two variables is unitless and always between -1 and +1.

Accepted Answer

Correlation coefficients are standardized measures, meaning they do not depend on the units of measurement, and they always range from -1 (perfect negative correlation) to +1 (perfect positive correlation).

Question 5

Correlation is a single-number summary of a scatterplot.

Accepted Answer

Correlation quantifies the degree to which two variables are related. It is a single number that describes the extent of the relationship between two variables, typically ranging from -1 to 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 indicates no correlation.

Question 6

Strongly related variables may have a correlation close to zero if the relationship is nonlinear.

Accepted Answer

Correlation measures the strength and direction of a linear relationship between two variables. If the relationship is nonlinear, even if it's strong, the correlation coefficient might be close to zero because it fails to capture the essence of the nonlinear relationship.

Question 7

Counts for a categorical variable are often expressed as percentages of the total.

Accepted Answer

Counts for a categorical variable can be converted to percentages to express the proportion of each category relative to the total, providing a clearer understanding of the distribution of categories within the data.

Question 8

The scatterplot is a graphical technique used to display the relationship between two numerical variables.

Accepted Answer

A scatterplot visually represents the relationship between two numerical variables by displaying data points on a two-dimensional graph, where each axis represents one of the variables.

Question 9

A trend line on a scatterplot is a line or a curve that "fits" the scatter as well as possible.

Accepted Answer

A trend line on a scatterplot, also known as a line of best fit, is indeed a line or curve that attempts to depict the relationship between the variables in the scatterplot as accurately as possible.

Question 10

We cannot attempt to interpret correlations numerically,with the one possible exception of indicating whether they are positive or negative.

Accepted Answer

Correlations can be interpreted numerically beyond just indicating whether they are positive or negative; the numerical value of a correlation coefficient (such as Pearson's r) indicates the strength of the relationship between two variables, with values closer to -1 or 1 indicating stronger relationships.

Question 11

If the standard deviations of X and Y are 15.5 and 10.8,respectively,and the covariance of X and Y is 128.8,then the correlation coefficient is approximately 0.77.

Accepted Answer

The correlation coefficient (r) is calculated using the formula r = covariance(X, Y) / (σX * σY), where σX and σY are the standard deviations of X and Y, respectively. Substituting the given values, r = 128.8 / (15.5 * 10.8) ≈ 0.77.

Question 12

We can use side-by-side boxplots to compare at most 2 distributions of numeric data.

Accepted Answer

Side-by-side boxplots can be used to compare more than two distributions of numeric data, allowing for the comparison of multiple groups simultaneously.

Question 13

The advantage that correlation has over covariance is that correlation has a set lower and upper limit.

Accepted Answer

Correlation values range from -1 to 1, providing a standardized measure of the strength and direction of a relationship between two variables, whereas covariance values are not standardized and can range indefinitely, making them less interpretable on their own.

Question 14

Correlation is affected by the measurement scales applied to the X and Y variables.

Accepted Answer

Correlation is a measure of the strength and direction of a linear relationship between two variables and is not affected by changes in the measurement scales of the variables, such as unit conversions.

Question 15

If the standard deviation of X is 15,the covariance of X and Y is 94.5,and the correlation is 0.90,then the variance of Y is 7.0.

Accepted Answer

The variance of Y can be calculated using the formula for correlation: $\rho_{X,Y} = \frac{cov(X,Y)}{\sigma_X \sigma_Y}$, where $\rho_{X,Y}$ is the correlation between X and Y, $cov(X,Y)$ is the covariance of X and Y, $\sigma_X$ is the standard deviation of X, and $\sigma_Y$ is the standard deviation of Y. Rearranging the formula to solve for $\sigma_Y^2$ (the variance of Y) gives us $\sigma_Y^2 = \frac{cov(X,Y)^2}{\rho_{X,Y}^2 \sigma_X^2}$. Plugging in the given values: $\sigma_Y^2 = \frac{94.5^2}{0.90^2 \times 15^2}$, which does not equal 7.

Question 16

The cutoff for defining a large correlation is 0.5.

Accepted Answer

The cutoff for defining a large correlation can vary depending on the context and the field of study, but commonly, a correlation above 0.7 is considered large in many social science contexts.

Question 17

To form a scatterplot of X versus Y,X and Y must be paired variables.

Accepted Answer

In a scatterplot of X versus Y, each point in the plot represents a pair of values, indicating that X and Y must be paired variables to correctly display their relationship.

Question 18

Side-by-side box plots allow you to quickly see how two or more categories of a numerical variable compare.

Accepted Answer

Side-by-side box plots are used to display the distribution of a numerical variable across different categories, making it easy to compare their central tendency, spread, and outliers.

Question 19

If the coefficient of correlation r = 0 .80,the standard deviations of X and Y are 20 and 25,respectively,then Cov(X,Y)must be 400.

Accepted Answer

The covariance can be calculated using the formula Cov(X,Y) = r * σx * σy. Substituting the given values: Cov(X,Y) = 0.80 * 20 * 25 = 400.

Question 20

Correlation and covariance can be used to examine relationships between numeric variables as well as for categorical variables that have been coded numerically.

Accepted Answer

Correlation and covariance are statistical measures used to examine relationships between numeric variables, not categorical variables, even if they are coded numerically.

Quiz 3: Finding Relationships Among Variables