Linear Regressions

Front

What is the correlation coefficient?

Back

The correlation coefficient (r) is a statistical measure that describes the strength and direction of a relationship between two variables.

Front

What does a correlation coefficient of r = -0.9 indicate?

Back

A correlation coefficient of r = -0.9 indicates a strong negative correlation between the two variables.

Front

How do you interpret a correlation coefficient of r = 1?

Back

A correlation coefficient of r = 1 indicates a perfect positive correlation, meaning as one variable increases, the other variable also increases.

Front

What is the formula for a linear regression equation?

Back

The formula for a linear regression equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope (m) in a linear regression equation represent?

Back

The slope (m) represents the rate of change of the dependent variable (y) for each unit change in the independent variable (x).

Front

If the linear regression equation is y = 61.93x - 1.79, what is the predicted value of y when x = 10?

Back

The predicted value of y when x = 10 is 617.5 miles.

Front

What type of correlation is indicated by a scatterplot with points that do not show any clear trend?

Back

A scatterplot with points that do not show any clear trend indicates no correlation.

Front

What does a positive correlation look like on a scatterplot?

Back

A positive correlation on a scatterplot shows that as one variable increases, the other variable also tends to increase, resulting in an upward trend.

Front

What is the significance of the y-intercept (b) in a linear regression equation?

Back

The y-intercept (b) is the value of y when x is 0; it represents the starting point of the line on the y-axis.

Front

How can you determine the strength of a correlation?

Back

The strength of a correlation can be determined by the absolute value of the correlation coefficient (r); values closer to 1 or -1 indicate stronger correlations.