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 it mean if r is close to 1?

Back

If r is close to 1, it indicates a strong positive correlation, meaning as one variable increases, the other variable also tends to increase.

Front

What does it mean if r is close to -1?

Back

If r is close to -1, it indicates a strong negative correlation, meaning as one variable increases, the other variable tends to decrease.

Front

What does it mean if r is close to 0?

Back

If r is close to 0, it indicates little to no correlation between the two variables, meaning changes in one variable do not predict changes in the other.

Front

How do you interpret a correlation coefficient of -0.999?

Back

A correlation coefficient of -0.999 indicates a very strong negative correlation between the two variables.

Front

How do you interpret a correlation coefficient of 0.998?

Back

A correlation coefficient of 0.998 indicates a very strong positive correlation between the two variables.

Front

What is direct variation?

Back

Direct variation is a relationship between two variables where one variable is a constant multiple of the other, expressed as y = kx, where k is a non-zero constant.

Front

If y varies directly as x and y = -7 when x = -14, what is the constant of variation (k)?

Back

The constant of variation (k) is 0.5, calculated as k = y/x = -7/-14.

Front

If y = kx and k = 0.5, what is y when x = 10?

Back

If k = 0.5 and x = 10, then y = 0.5 * 10 = 5.