Covariance and Correlation Questionbank

Whether it makes sense to generalize beyond the sample

Whether the calculation was done manually or by a computer

Whether the points are colored consistently on the plot

Whether the variables have the same units of measurement

The student is correct, because a correlation coefficient very close to $-1$ is sufficient evidence that the relationship is linear.

The student is correct, provided that the sample size is large enough for the result to be statistically significant.

The student is incorrect, because a high correlation coefficient can still be produced by certain non-linear data patterns.

The student is incorrect, because a correlation coefficient of $-0.96$ indicates a very weak relationship between the variables.

The data points lie on a curved line rather than a straight line

The apparent relationship is a coincidence due to a small sample size

The correlation coefficient was calculated using the population-style formula

The variables were measured using different units of measurement

A set of data that has been categorized into two distinct groups or clusters.

A list of values for a single variable collected over two different time periods.

Any data set that results in a correlation coefficient between $-1$ and $1$.

Data consisting of pairs of values where two quantitative variables are measured for each case.

Moderate positive linear relationship

No relationship of any kind

Very weak negative linear relationship

Strong negative linear relationship

0.00

-1.00

-0.25

0.25

Calculating the average of the differences between each value and its respective mean

Taking the square root of the sum of squared deviations for both variables

Subtracting the product of the means from the average of the product of the variables

Dividing the covariance by the product of the standard deviations of both variables

$4$

$\frac{4}{3}$

$\frac{2}{3}$

$2$

$r$

$100r$

$0.01r$

$10000r$

Both variables must be quantitative.

Both variables must be categorical.

The relationship between the variables must be non-linear.

The correlation coefficient $r$ is resistant to the influence of outliers.