least squares regression line

Front

What is the least squares regression line?

Back

The least squares regression line is a statistical method used to determine the best-fitting line through a set of data points by minimizing the sum of the squares of the vertical distances (residuals) between the observed values and the values predicted by the line.

Front

How do you make a prediction using the regression line?

Back

To make a prediction using the regression line, you plug in a value for x (the independent variable) into the regression equation and simplify to find the predicted value of y (y-hat).

Front

What does a correlation indicate about two variables?

Back

A correlation indicates that two variables are related, but it does not imply causation.

Front

What does a negative correlation mean?

Back

A negative correlation means that as one variable increases, the other variable decreases.

Front

What is extrapolation in the context of regression?

Back

Extrapolation is the use of a regression line for prediction outside the interval of x values used to obtain the line.

Front

What is the purpose of a scatter plot in regression analysis?

Back

A scatter plot visually represents the relationship between two variables, helping to identify patterns, trends, and correlations.

Front

What does it mean if a scatter plot shows no association?

Back

If a scatter plot shows no association, it means there is no discernible pattern or relationship between the two variables.

Front

What is the formula for the least squares regression line?

Back

The formula for the least squares regression line is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the slope in a regression line?

Back

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

Front

What does the y-intercept represent in a regression line?

Back

The y-intercept (b) represents the predicted value of y when x is zero.