R Tutorial: Linear regression - the fundamental method

Key Takeaways

let's start with the most basic regression algorithm linear regression linear regression assumes that the expected outcome is the weighted sum of all the inputs it also assumes that the change in Y is linearly proportional to the change in any X this is the simplest of the regression methods in our cricket example linear regression assumes that temperature is directly proportional to cricket chirp rate it are you fit a linear regression model using the LM function this function takes as arguments a formula that describes the model you want to fit and the data here the data is in the data frame cricket with an outcome column temperature and an input column trips per second a formula in R is designated by a twiddle or tilt the left hand side of the formula is the outcome you want to predict such as temperature or blood pressure the right hand side of the formula holds the input variables you can concatenate multiple input variables with a plus sign to convert a string into a formula use the s formula function print the model to look at its structure you will see a report on the coefficients or betas of the model the intercept is beta 0 the value of the model when all the inputs are 0 the other coefficients are the weights for the weighted sum of the variables in this example the coefficient for trips per second is just over 3 that means 2 things first the sign of the coefficient is positive so temperature should increase as trip rate increases second for every unit increase in chirp rate the temperature should increase by little over 3 degrees if everything else is held constant you can get the model Diagnostics by calling summary on the model summary includes not only the values of the coefficients but the standard error in their estimated value along with other Diagnostics we will cover some of these Diagnostics in a later chapter but for now just know that they are available to get these Diagnostics conveniently packaged in a data frame use the glance function from the package broom for the R squared diagnostic you can also use the function R app F test from the package sigur now let's do some exercises to review what you've learned