Linear Regression

Front

What is the equation of a linear regression line?

Back

The equation of a linear regression line is typically written as 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 change in the dependent variable (y) for a one-unit change in the independent variable (x).

Front

What is the purpose of a best-fit line in linear regression?

Back

The best-fit line is used to make predictions about the dependent variable based on the independent variable.

Front

How do you interpret 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

What is the formula for calculating the linear regression line using the least squares method?

Back

The least squares method minimizes the sum of the squares of the residuals (the differences between observed and predicted values).

Front

What is the significance of rounding decimals in linear regression equations?

Back

Rounding decimals in linear regression equations helps simplify the equation for easier interpretation and application.

Front

How can you use a linear regression equation to make predictions?

Back

You can substitute a value for x into the linear regression equation to calculate the corresponding predicted value of y.

Front

What does it mean if the slope of a linear regression line is negative?

Back

A negative slope indicates an inverse relationship between the independent variable (x) and the dependent variable (y); as x increases, y decreases.

Front

What is the role of the independent variable in a linear regression model?

Back

The independent variable (x) is the variable that is manipulated or changed to observe its effect on the dependent variable (y).

Front

What is the role of the dependent variable in a linear regression model?

Back

The dependent variable (y) is the outcome or response variable that is measured to see how it is affected by changes in the independent variable (x).