R-Square: This is known as the coefficient of determination.Here is how to interpret the rest of the model output: For example, a student who studies for 4 hours and takes 1 prep exam is expected to score a 89.31 on the exam:Įxam score = 67.67 + 5.56*(4) -0.60*(1) = 89.31 We can also use this model to find the expected exam score a student will receive based on their total hours studied and prep exams taken. Each additional one unit increase in prep exams taken is associated with an average decrease of 0.60 points in exam score, assuming hours studied is held constant.Each additional one unit increase in hours studied is associated with an average increase of 5.56 points in exam score, assuming prep exams is held constant.The way to interpret the coefficients are as follows: Note: The screenshot below shows multiple linear regression output for Excel, but the numbers shown in the output are typical of the regression output you’ll see using any statistical software.įrom the model output, the coefficients allow us to form an estimated multiple linear regression model:Įxam score = 67.67 + 5.56*(hours) – 0.60*(prep exams) The following screenshot shows what the multiple linear regression output might look like for this model: Suppose we fit a multiple linear regression model using the predictor variables hours studied and prep exams taken and a response variable exam score. How to Interpret Multiple Linear Regression Output Fortunately, any statistical software can calculate these coefficients for you. The method used to find these coefficient estimates relies on matrix algebra and we will not cover the details here. ŷ i: The predicted response value based on the multiple linear regression model.y i: The actual response value for the i th observation.The values for β 0, β 1, B 2, …, β p are chosen using the least square method, which minimizes the sum of squared residuals (RSS): β j: The average effect on Y of a one unit increase in X j, holding all other predictors fixed.If we have p predictor variables, then a multiple linear regression model takes the form:

However, if we’d like to understand the relationship between multiple predictor variables and a response variable then we can instead use multiple linear regression. When we want to understand the relationship between a single predictor variable and a response variable, we often use simple linear regression.

Multiple linear regression