Exploring Two–Variable Data

The exam scores tend to stay constant regardless of how many hours are studied since they are perfectly uncorrelated.

The number of hours studied causes lower exam scores with near certainty due to causation implied by high correlation.

There exists no significant relationship between hours studied and exam scores because correlations near -1 indicate lack of association.

There exists a strong negative linear relationship between hours studied and exam scores.

There might be an outlier influencing the high correlation coefficient observed.

The value of $r$ may change if more data points are added, altering the conclusion.

The presence of confounding variables may affect both the hours studied and exam scores.

The sample size for the study could be too small to establish a strong correlation.

No linear relationship.

A perfect negative linear relationship.

The data points all fall perfectly on a line.

A perfect positive linear relationship.

-1

Exactly zero

Greater than zero

One

It may lead to an underestimate of r for low values and overestimate at high values.

Heteroscedasticity does not affect Pearson's r calculations or interpretations.

It will cause an underestimation in r only at higher value ranges.

It will result in a consistently overestimated r across all ranges.

Histogram

Bar graph

Scatterplot

Pie chart

Close to 1

Close to 0

Close to -1

Impossible to determine

Variable X causes decreases in variable Y due to an inverse causation effect indicated by r-value alone.

Variable X has no apparent effect on variable Y since r-values only measure linear relationships.

Variable X has an inconsistent effect on variable Y since negative values signify unreliable results in correlations.

Variable X has a strong negative linear association with variable Y.

One (1)

Less than zero (- values)

Zero (0)

Cannot be calculated

The variance of Y given X.

The coefficient of determination.

The slope of least squares regression line.