Scatterplots and correlation coefficient

Front

What is a scatterplot?

Back

A scatterplot is a graphical representation of two variables, showing the relationship between them using points on a Cartesian plane.

Front

What does the correlation coefficient (r) indicate?

Back

The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, ranging from -1 to 1.

Front

What does an r value of -0.98 indicate about the correlation?

Back

An r value of -0.98 indicates a strong negative correlation, meaning as one variable increases, the other decreases significantly.

Front

What does an r value of 0.5 indicate about the correlation?

Back

An r value of 0.5 indicates a moderate positive correlation, meaning as one variable increases, the other tends to increase as well.

Front

What does an r value of 0 indicate?

Back

An r value of 0 indicates no correlation between the two variables, meaning there is no predictable relationship.

Front

How do you interpret a weak negative correlation?

Back

A weak negative correlation (e.g., r = -0.26) suggests that there is a slight tendency for one variable to decrease as the other increases, but the relationship is not strong.

Front

If y varies directly as x, what is the relationship between y and x?

Back

If y varies directly as x, it means that y = kx for some constant k, indicating that y increases or decreases proportionally with x.

Front

Given y = -7 when x = -14, find k in the direct variation equation y = kx.

Back

k = y/x = -7 / -14 = 0.5.

Front

If y = kx and k = 0.5, what is y when x = 20?

Back

y = 0.5 * 20 = 10.

Front

What is the difference between strong positive and weak positive correlation?

Back

Strong positive correlation (e.g., r close to 1) indicates a clear, consistent relationship where both variables increase together, while weak positive correlation (e.g., r around 0.2) indicates a less consistent relationship.