when interpreting the results of multiple regression beta coefficients are valid while holding all other variables constant all else equal the output from a multiple regression can be displayed horizontally as an equation or vertically in table form 
example of how to use multiple linear regression mlr as an example an analyst may want to know how the movement of the market affects the price of exxonmobil xom in this case the linear equation will have the value of the s p 500 index as the independent variable or predictor and the price of xom as the dependent variable in reality multiple factors predict the outcome of an event the price movement of exxonmobil for example depends on more than just the performance of the overall market other predictors such as the price of oil interest rates and the price movement of oil futures can affect the price of exon mobil xom and the stock prices of other oil companies to understand a relationship in which more than two variables are present mlr is used mlr is used to determine a mathematical relationship among several random variables 3 in other terms mlr examines how multiple independent variables are related to one dependent variable once each of the independent factors has been determined to predict the dependent variable the information on the multiple variables can be used to create an accurate prediction on the level of effect they have on the outcome variable the model creates a relationship in the form of a straight line linear that best approximates all the individual data points referring to the mlr equation above in our example the least squares estimates b0 b1 b2 bp are usually computed by statistical software as many variables can be included in the regression model in which each independent variable is differentiated with a number 1 2 3 4 p multiple regression can also be non linear in which case the dependent and independent variables would not follow a straight line the multiple regression model allows an analyst to predict an outcome based on information provided on multiple explanatory variables still the model is not always perfectly accurate as each data point can differ slightly from the outcome predicted by the model the residual value e which is the difference between the actual outcome and the predicted outcome is included in the model to account for such slight variations we ran our xom price regression model through a statistics computation software it returned this output image by sabrina jiang investopediaan analyst would interpret this output to mean if other variables are held constant the price of xom will increase by 7 8 if the price of oil in the markets increases by 1 the model also shows that the price of xom will decrease by 1 5 following a 1 rise in interest rates r2 indicates that 86 5 of the variations in the stock price of exxon mobil can be explained by changes in the interest rate oil price oil futures and s p 500 index the difference between linear and multiple regressionordinary linear squares ols regression compares the response of a dependent variable given a change in some explanatory variables however a dependent variable is rarely explained by only one variable in this case an analyst uses multiple regression which attempts to explain a dependent variable using more than one independent variable multiple regressions can be linear and nonlinear mlrs are based on the assumption that there is a linear relationship between both the dependent and independent variables it also assumes no major correlation between the independent variables 