Correlation Coefficient and Line of Best Fit

Front

What is the correlation coefficient?

Back

A statistical measure that describes the strength and direction of a relationship between two variables, ranging from -1 to 1.

Front

What does a correlation coefficient of 1 indicate?

Back

A perfect positive linear relationship between two variables.

Front

What does a correlation coefficient of -1 indicate?

Back

A perfect negative linear relationship between two variables.

Front

What does a correlation coefficient of 0 indicate?

Back

No linear relationship between the two variables.

Front

What is the line of best fit?

Back

A straight line that best represents the data on a scatter plot, used to predict values.

Front

How do you determine the slope of the line of best fit?

Back

By calculating the change in y over the change in x (rise over run) between two points on the line.

Front

What does a strong negative correlation (e.g., r = -0.89) imply?

Back

As one variable increases, the other variable tends to decrease significantly.

Front

What does a weak positive correlation (e.g., r = 0.25) imply?

Back

There is a slight tendency for one variable to increase as the other increases, but the relationship is not strong.

Front

How can you use the line of best fit to make predictions?

Back

By substituting a value of x into the equation of the line to find the corresponding y value.

Front

What is the formula for the line of best fit in slope-intercept form?

Back

y = mx + b, where m is the slope and b is the y-intercept.