# Simple linear regression in excel for mac Contents:

An Excel sheet with both the data and the results can be downloaded by clicking on the button below: Download the data The data have been obtained in Lewis T. Using simple linear regression, we want to find out how the weight of the children varies with their height, and to verify if a linear model makes sense. Select the data on the Excel sheet.

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In our case; the Dependent variable or variable to model is the "Weight". The quantitative explanatory variable is the "Height". As the column header was selected for the variables, the Variable labels option needs to be activated. The results will then be displayed. The first table displays the goodness of fit coefficients of the model. The remainder of the variability is due to some effects other explanatory variables that have not been included in this analysis. It is important to examine the results of the analysis of variance table see below.

The results enable us to determine whether or not the explanatory variables bring significant information null hypothesis H0 to the model. In other words, it's a way of asking yourself whether it is valid to use the mean to describe the whole population, or whether the information brought by the explanatory variable s is of value or not. Given the fact that the probability corresponding to the F value is lower than 0. Therefore, we can conclude with confidence that the three variables do bring a significant amount of information. The following table gives details on the model.

This table is helpful when predictions are needed, or when you need to compare the coefficients of the model for a given population with the ones obtained for another population. The equation of the model is written below the table. We can see that in the range of the variable Height that is taken into account here, when the Height increases by one inch, the Weight increases by 3.

The next table shows the residuals. It enables us to take a closer look at each of the standardized residuals. Here's how:. This will add the Data Analysis tools to the Data tab of your Excel ribbon. In this example, we are going to do a simple linear regression in Excel. What we have is a list of average monthly rainfall for the last 24 months in column B, which is our independent variable predictor , and the number of umbrellas sold in column C, which is the dependent variable. Of course, there are many other factors that can affect sales, but for now we focus only on these two variables:.

With Analysis Toolpak added enabled, carry out these steps to perform regression analysis in Excel:. If you are building a multiple regression model, select two or more adjacent columns with different independent variables.

## Statistics the Mac Way | AnalystSoft | StatPlus:mac | StatPlus | BioStat | StatFi

As you have just seen, running regression in Excel is easy because all calculations are preformed automatically. The interpretation of the results is a bit trickier because you need to know what is behind each number. Below you will find a breakdown of 4 major parts of the regression analysis output.

This part tells you how well the calculated linear regression equation fits your source data.

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6. How to Run Regression Analysis in Microsoft Excel (with Sample Analyses)!

Multiple R. The correlation coefficient can be any value between -1 and 1, and its absolute value indicates the relationship strength. The larger the absolute value, the stronger the relationship:. R Square. It is the Coefficient of Determination , which is used as an indicator of the goodness of fit. It shows how many points fall on the regression line. The R 2 value is calculated from the total sum of squares, more precisely, it is the sum of the squared deviations of the original data from the mean.

In our example, R 2 is 0. Adjusted R Square. It is the R square adjusted for the number of independent variable in the model.

### Regression analysis in Excel - the basics

You will want to use this value instead of R square for multiple regression analysis. Standard Error. It is another goodness-of-fit measure that shows the precision of your regression analysis - the smaller the number, the more certain you can be about your regression equation. While R 2 represents the percentage of the dependent variables variance that is explained by the model, Standard Error is an absolute measure that shows the average distance that the data points fall from the regression line.

Basically, it splits the sum of squares into individual components that give information about the levels of variability within your regression model:. The ANOVA part is rarely used for a simple linear regression analysis in Excel, but you should definitely have a close look at the last component. The Significance F value gives an idea of how reliable statistically significant your results are. If Significance F is less than 0. If it is greater than 0. This section provides specific information about the components of your analysis:.

The most useful component in this section is Coefficients. For our data set, where y is the number of umbrellas sold and x is an average monthly rainfall, our linear regression formula goes as follows:. For example, with the average monthly rainfall equal to 82 mm, the umbrella sales would be approximately In a similar manner, you can find out how many umbrellas are going to be sold with any other monthly rainfall x variable you specify. If you compare the estimated and actual number of sold umbrellas corresponding to the monthly rainfall of 82 mm, you will see that these numbers are slightly different:.

Why's the difference? Because independent variables are never perfect predictors of the dependent variables. And the residuals can help you understand how far away the actual values are from the predicted values:. For the first data point rainfall of 82 mm , the residual is approximately So, we add this number to the predicted value, and get the actual value: If you need to quickly visualize the relationship between the two variables, draw a linear regression chart.

That's very easy! This will insert a scatter plot in your worksheet, which will resemble this one: Now, we need to draw the least squares regression line. To have it done, right click on any point and choose Add Trendline… from the context menu. On the right pane, select the Linear trendline shape and, optionally, check Display Equation on Chart to get your regression formula:. As you may notice, the regression equation Excel has created for us is the same as the linear regression formula we built based on the Coefficients output.

For example, you can choose a different line color and use a solid line instead of a dashed line select Solid line in the Dash type box : At this point, your chart already looks like a decent regression graph:. And this is how our improved regression graph looks like:.

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• Linear regression analysis in Excel.
• The LINEST function uses the least squares regression method to calculate a straight line that best explains the relationship between your variables and returns an array describing that line. You can find the detailed explanation of the function's syntax in this tutorial. For now, let's just make a formula for our sample dataset:. The formula returns the b coefficient E1 and the a constant F1 for the already familiar linear regression equation:. If you avoid using array formulas in your worksheets, you can calculate a and b individually with regular formulas:. Additionally, you can find the correlation coefficient Multiple R in the regression analysis summary output that indicates how strongly the two variables are related to each other:.

The following screenshot shows all these Excel regression formulas in action:. To have a closer look at our linear regression formulas and other techniques discussed in this tutorial, you are welcome to download our sample Regression Analysis in Excel workbook. That's how you do linear regression in Excel. That said, please keep in mind that Microsoft Excel is not a statistical program. For the regression analysis.. Please advise.. Thanks Ms. Svetlana for the quick response. Your tutorial was very easy to understand as it went step by step, hand holding a novice..

I really appreciate your effort in making complex issues simple. Do you have similar tutorial on Multiple regression, Pricing optimization ,Price bundling etc in Excel , Decision tree Analysis etc. Would appreciate your advise. Regards Shankar. So I completed the regression analysis for my assignment.

So how do I figure out what actually goes on the graph? I tried two different sets of data, one produced two points on the graph and the other did not produce anything close to what your examples were. Why does of observations equal data points minus 1? It is not immediately apparent in your example because you include the title rows in your input ranges.

Besides this one issue the article is great and extremely informative. Hi Braden, It's a very good question. I included the header row in the input ranges to make it easier to interpret the regression analysis output, based on the column headers. The number of observations equals the number of data points 24 observations, rows ; the header row is not counted because the Labels box was selected.

Excel Walkthrough 4 - Reading Regression Output

That is, 6. The Significance F value measures the reliability of the results. If it is less than 0. Svetlana, Congratulations for great work on this topic. You made it easy to understand in short time. I have two variables say time and one predictor variable. However, the predictor variable is classified into regions. Is there a possibility of having that captured in a regression output as a grouping variable in excel?

Your post is amazing; it must have helped millions including me. One simple confusion; now i can i forecast using this regression concept. So if have to predict future, i can use this concept. Many thanks in advance. Hi Svetlana, Thanks for your detailed and well-written article on regression in the Analysis Toolpak and also for mentioning RegressIt as a professional-grade alternative.

I'd like your readers to know that RegressIt is free unlike XLSTAT and has many features that are designed to help users learn and apply best practices of regression modeling. Variables are selected from a list of names rather than by entering coordinates of cell ranges , and there are tools for testing model assumptions, comparing models side by side, and sharing results with others in presentation quality format.

The graphs and tables that it produces are far superior to what you get with the Analysis Toolpak, both in terms of design and in terms of the set of options that are available. RegressIt also includes very detailed built-in teaching notes that can be embedded in the model worksheets, and it has features that help instructors to grade and verify the originality of work submitted by students. Also, unlike the Analysis Toolpak, it has the capability to forecast from a regression model including an option for interactive confidence limits on forecast charts , which addresses the question raised by one of your respondents Syed, post And one more thing: it includes a user-friendly interface with R that allows users to run both linear and logistic regression models in R without writing any code.

This feature allows more sophisticated model testing to be carried out and provides a gentle introduction to the R environment for those without programming experience. I encourage you to mention some of these features to your readers, either in this list of comments or a separate post. Cheers, --Bob.