Statistics: 4.3 Linear Regression

Front

What is linear regression?

Back

A statistical method used to model the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data.

Front

What does the slope in a linear regression equation represent?

Back

The rate of change of the dependent variable for each unit change in the independent variable.

Front

What is the y-intercept in a linear regression equation?

Back

The value of the dependent variable when the independent variable is zero.

Front

How do you interpret a negative correlation?

Back

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

Front

What is the purpose of the least squares method in linear regression?

Back

To minimize the sum of the squares of the residuals (the differences between observed and predicted values).

Front

What does a correlation coefficient of -1 indicate?

Back

A perfect negative linear relationship between two variables.

Front

What is the formula for a simple linear regression equation?

Back

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

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How can you determine if a linear regression model is a good fit for the data?

Back

By analyzing the R-squared value, residual plots, and checking for patterns in the residuals.

Front

What does it mean if the R-squared value is close to 1?

Back

It indicates that a large proportion of the variance in the dependent variable is explained by the independent variable.

Front

What is multicollinearity in the context of linear regression?

Back

A situation where two or more independent variables are highly correlated, which can affect the stability of the regression coefficients.