Fitting Linear Regression Models
When working with data, you often want to predict a numeric value using other variables. For instance, you might want to estimate a person's weight based on their height, or predict house prices from features like square footage and number of bedrooms. Linear regression is a fundamental statistical modeling technique that allows you to quantify the relationship between a numeric outcome (the dependent variable) and one or more predictors (the independent variables). In R, the lm() function is the standard tool for fitting linear regression models.
1234567891011# Create a data frame with height and weight df <- data.frame( height = c(60, 62, 65, 68, 70, 72), weight = c(115, 120, 135, 150, 165, 180) ) # Fit a linear regression model lm_model <- lm(weight ~ height, data = df) # Inspect the model summary(lm_model)
The formula interface in lm() uses the syntax outcome ~ predictor1 + predictor2, where the variable to be predicted is on the left of the tilde (~), and the predictors are on the right. In the example, weight ~ height means you are modeling weight as a function of height. The data argument specifies which data frame contains these variables, making your code concise and readable.
The returned object from lm() is a model object containing all details about the fitted regression, including the estimated coefficients, model diagnostics, and residuals. You can extract information from this object using functions like summary(), coef(), and residuals().
- Factor variables are automatically handled as categorical predictors, but you should check that categorical data are correctly coded as factors;
- Missing data in predictors or the outcome will cause those rows to be dropped from the model, which can affect your results;
- Coefficients represent the effect of a one-unit increase in the predictor, holding other variables constant, but be careful when interpreting coefficients for categorical predictors or when predictors are correlated.
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When working with data, you often want to predict a numeric value using other variables. For instance, you might want to estimate a person's weight based on their height, or predict house prices from features like square footage and number of bedrooms. Linear regression is a fundamental statistical modeling technique that allows you to quantify the relationship between a numeric outcome (the dependent variable) and one or more predictors (the independent variables). In R, the lm() function is the standard tool for fitting linear regression models.
1234567891011# Create a data frame with height and weight df <- data.frame( height = c(60, 62, 65, 68, 70, 72), weight = c(115, 120, 135, 150, 165, 180) ) # Fit a linear regression model lm_model <- lm(weight ~ height, data = df) # Inspect the model summary(lm_model)
The formula interface in lm() uses the syntax outcome ~ predictor1 + predictor2, where the variable to be predicted is on the left of the tilde (~), and the predictors are on the right. In the example, weight ~ height means you are modeling weight as a function of height. The data argument specifies which data frame contains these variables, making your code concise and readable.
The returned object from lm() is a model object containing all details about the fitted regression, including the estimated coefficients, model diagnostics, and residuals. You can extract information from this object using functions like summary(), coef(), and residuals().
- Factor variables are automatically handled as categorical predictors, but you should check that categorical data are correctly coded as factors;
- Missing data in predictors or the outcome will cause those rows to be dropped from the model, which can affect your results;
- Coefficients represent the effect of a one-unit increase in the predictor, holding other variables constant, but be careful when interpreting coefficients for categorical predictors or when predictors are correlated.
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