Last Update: February 21, 2022
Simple linear regression is used to model linear relationship between two variables and . Dependent variable is the explained one which is also known as target or response feature. Independent variable is the explanatory one which is also known as predictor feature.
When doing simple linear regression, we can start by drawing a scatter chart with variables and on the vertical and horizontal axis, respectively. Then, we can draw a line which describes linear relationship between variables and . This line represents model fitting with formula . Notice that we are using ˄ or hat character in formula notation because they are estimates. Regression fitted values are the estimated values. Estimated constant or intercept coefficient is the value when or the value where line crosses vertical axis. Estimated slope coefficient is the estimated change in when changes in one unit.
Model fitting can be done using ordinary least squares method with formula . This method minimizes the sum of squared estimated regression residuals . Estimated regression residuals with formula are the differences between actual and fitted values.
Below, we find an example of scatter chart with simple linear regression of house price explained by its lot size .
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 Data Description: Sales prices of houses sold in the city of Windsor, Canada, during July, August and September, 1987.
Original Source: Anglin, P., and Gencay, R. (1996). Semiparametric Estimation of a Hedonic Price Function. Journal of Applied Econometrics, 11, 633–648.
Source: AER R package HousePrices object. Christian Kleiber and Achim Zeileis. (2008). Applied Econometrics with R. Springer-Verlag, New York.