It tells us whether or not the regression model as a whole is statistically significant. This is the p-value associated with the overall F statistic. This is the overall F statistic for the regression model, calculated as regression MS / residual MS. The total sample size of the dataset used to produce the regression model.į: 23.46. In this example, the observed values fall an average of 5.366 units from the regression line. This is the average distance that the observed values fall from the regression line. This value will also be less than the value for R Square and penalizes models that use too many predictor variables in the model. This represents the R Square value, adjusted for the number of predictor variables in the model. In this example, 73.4% of the variation in the exam scores can be explained by the number of hours studied and the number of prep exams taken.Īdjusted R Square: 0.703. It is the proportion of the variance in the response variable that can be explained by the explanatory variables. This is known as the coefficient of determination. This represents the multiple correlation between the response variable and the two predictor variables. Here is how to interpret the most important values in the output: The following screenshot shows the regression output of this model in Excel: To explore this relationship, we can perform multiple linear regression using hours studied and prep exams taken as predictor variables and exam score as a response variable. Suppose we want to know if the number of hours spent studying and the number of prep exams taken affects the score that a student receives on a certain college entrance exam. Example: Interpreting Regression Output in Excel This tutorial explains how to interpret every value in the output of a multiple linear regression model in Excel. QI Macros also performs Multiple Regression Analysis and Binary Logistic Regression Analysis.Multiple linear regression is one of the most commonly used techniques in all of statistics. This provides you with information on how the confidence level can impact your results, depending on where alpha is set. The 95% and 99% Confidence Levels reference when your alpha value is set at. NOTE: The straight lines found in your first chart (Salt concentration) represent the Upper and Lower Prediction Intervals, while the more curved lines are the Upper and Lower Confidence IntervalsĬonfidence Intervals provide a view into the uncertainty when estimating the mean, while Prediction Intervals account for variation in the Y values around the mean. In addition to the Summary Output above, QI Macros also calculates Residuals and Probability Data and creates scatter plots in Excel for you: Residuals Output, Probability Output and Charts For example, if the % of paved roadway = 1% the Salt concentration could be estimated as 17.547* (1%) +2.6765 = 20.2235 mg/l. Using the equation, y = Salt concentration = 2.677 + 17.547*(% paved roadway area), you could predict the salt concentration based on the percent of paved roadway. Use the Equation for Prediction and Estimation In other words, there is a relation between the two variables. Since the p value ( 0 < 0.05), we "Reject the Null Hypothesis" that the two variables are unrelated. 951 means that 95.1% of the variation in salt concentration can be explained by roadway area. Some statistics references recommend using the Adjusted R Square value. Evaluate the R Square value (0.951)Īnalysis: If R Square is greater than 0.80, as it is in this case, there is a good fit to the data. NOTE: If the first cell of your y values column is blank, that column of data will be omitted from your Regression output. QI Macros will automatically perform the regression analysis calculations for you:. Next, select your data and click on QI Macros > Statistical Tools > Regression & Other Statistics > Regression:.Enter your data into Excel with the independent variable in the left column and the dependent variable in the right column.This sample data is found in QI Macros Test Data > statistical.xlsx > Regression Data: What if we wanted to know if the salt concentration in runoff (dependent variable) is related to the percent of paved roadway area (independent variable). Regression arrives at an equation to predict performance based on each of the inputs. The purpose of regression analysis is to evaluate the effects of one or more independent variables on a single dependent variable. You Don't Have to be a Expert to Run Regression Analysis! QI Macros will do the math and analysis for you.Click on QI Macros menu > Statistical Tools > Regression.Free Agile Lean Six Sigma Trainer Training.Animated Lean Six Sigma Video Tutorials.Statistical Analysis - Hypothesis Testing.
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