So, for my example, I had 49 participants. This is just the number of subjects in the test. Observationsįinally, we have the number of observations. The smaller the standard error, the more precise the linear regression model is. This means, on average, my observed values were 4.31 kg from the regression line. So, here my standard error is 4.31 kg, when rounded. What’s useful about the standard error is that it is in the same units as the dependent variable. The standard error of the regression is the average distance that the observed values fall from the regression line. Usually, this value is only relevant when you are performing multiple linear regression, where there are more than 1 independent variables in the model. The adjusted R square takes into account the number of independent variables in the regression analysis, and corrects for bias. The other 57% of the variance is therefore caused by other factors, such as measurements errors. So, for my example, I can say that 43% of the variance in weight can be accounted for by the height measures. Researchers often multiple this value by 100 to get a percentage value. The R square value tells you how much variance the dependent variable can be accounted for by the values of the independent variable. To get this value, you simple square the multiple R value. You may sometimes see the R square being referred to as the coefficient of determination. If you’re interested to learn more about correlation, then I suggest you refer to the What is Pearson Correlation post. Briefly, it is a value that tells you how strong the linear relationship is.Ī value of 0.65 in this case indicates a fairly strong linear correlation between height and weight measures. This is the absolute value of the correlation coefficient between the two variables of interest. In the first table called Summary Output, there are some regression statistics from the test. I’ll now break down the output and go through each in more detail. Interpretation of the linear regression resultsĭepending on the options selected in the set-up window, you will have quite a lot of information in the results sheet. Line Fit Plots – will create another scatter graph where the Y and X variables are plotted, but it will also add the predicted Y values onto the graphįinally, the Normal Probability Plots option plots another scatter plot, which is used to determine whether the Y variable data fits a normal distribution.Residual Plots – will create a scatter graph where the residuals are plotted on the Y axis and the X variable is plotted on the X axis.Standardized Residuals – will return the standardized residuals these values can be useful when identifying potential outliers.Residuals – will return the list of predicted dependent values, based on the regression line, as well as the residual values for each point.The final set of options concerns the residuals in the analysis. New Workbook – lets you save the results in an entirely separate workbookįor my example, I’m going to select the second option and have the results placed in a new worksheet.New Worksheet Ply – lets you place the results in a new worksheet.

Output Range – you can highlight where you want the results to be placed in that worksheet.Output optionsįor the Output Options, you can specify where you want the regression results to be placed. However, if you want to use a different confidence level than 95%, then you need to select this option and enter the desired value here. By default, the results will return the 95% confidence intervals without having to change any options. It is also possible to specify the confidence level for the test. Generally, for linear regression, this option is not selected, so I will leave it unchecked for this example. Doing so would mean there is no Y intercept in the model. The next option called Constant is Zero is used if you want the regression line to start at 0, otherwise known as the origin. If you didn’t have any labels when you selected your data, then you should not tick this option. If you have highlighted the labels of the columns when selecting the data, then tick the Labels options. Input X Range – this is the data for the X variable, otherwise known as the independent variable.The Y variable is the one that you want to predict in the regression model. Input Y Range – this is the data for the Y variable, otherwise known as the dependent variable.To perform the linear regression, click on the Data Analysis button. Performing the linear regression in Excel We are now ready to perform the linear regression in Excel.

Excel data analysis regression exclude