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» Regression Analysis. Regression Analysis in Excel You Don't Have to be a Statistician to Run Regression Analysis. The purpose of regression analysis is to evaluate the effects of one or more independent variables on a single dependent variable. Regression arrives at an equation to predict performance based on each of the inputs. Mar 22, 2015 How to do regression analysis in Excel 2011 (Mac) - since there is no Microsoft Toolpak add-in or plug-in. Steps to setup, start and use StatPlus, the free supplemental software available to. 2012-11-22  Tech support scams are an industry-wide issue where scammers trick you into paying for unnecessary technical support services. You can help protect yourself from scammers by verifying that the contact is a Microsoft Agent or Microsoft Employee and that the phone number is an official Microsoft global customer service number.

In regression analysis, those factors are called variables. You have your dependent variable — the main factor that you’re trying to understand or predict. In Redman’s example above, the dependent variable is monthly sales. And then you have your independent variables — the factors you suspect have an impact on your dependent variable.

How does it work?

In order to conduct a regression analysis, you gather the data on the variables in question. (Reminder: you likely don’t have to do this yourself, but it’s helpful for you to understand the process your data analyst colleague uses.) You take all of your monthly sales numbers for, say, the past three years and any data on the independent variables you’re interested in. So, in this case, let’s say you find out the average monthly rainfall for the past three years as well. Then you plot all of that information on a chart that looks like this:

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The y-axis is the amount of sales (the dependent variable, the thing you’re interested in, is always on the y-axis) and the x-axis is the total rainfall. Each blue dot represents one month’s data—how much it rained that month and how many sales you made that same month.

Glancing at this data, you probably notice that sales are higher on days when it rains a lot. That’s interesting to know, but by how much? If it rains 3 inches, do you know how much you’ll sell? What about if it rains 4 inches?

Now imagine drawing a line through the chart above, one that runs roughly through the middle of all the data points. This line will help you answer, with some degree of certainty, how much you typically sell when it rains a certain amount.

This is called the regression line and it’s drawn (using a statistics program like SPSS or STATA or even Excel) to show the line that best fits the data. In other words, explains Redman, “The red line is the best explanation of the relationship between the independent variable and dependent variable.”

In addition to drawing the line, your statistics program also outputs a formula that explains the slope of the line and looks something like this:

Ignore the error term for now. It refers to the fact that regression isn’t perfectly precise. Just focus on the model:

What this formula is telling you is that if there is no “x” then Y = 200. So, historically, when it didn’t rain at all, you made an average of 200 sales and you can expect to do the same going forward assuming other variables stay the same. And in the past, for every additional inch of rain, you made an average of five more sales. “For every increment that x goes up one, y goes up by five,” says Redman.

Now let’s return to the error term. You might be tempted to say that rain has a big impact on sales if for every inch you get five more sales, but whether this variable is worth your attention will depend on the error term. A regression line always has an error term because, in real life, independent variables are never perfect predictors of the dependent variables. Rather the line is an estimate based on the available data. So the error term tells you how certain you can be about the formula. The larger it is, the less certain the regression line.

The above example uses only one variable to predict the factor of interest — in this case rain to predict sales. Typically you start a regression analysis wanting to understand the impact of several independent variables. So you might include not just rain but also data about a competitor’s promotion. “You keep doing this until the error term is very small,” says Redman. “You’re trying to get the line that fits best with your data.” While there can be dangers to trying to include too many variables in a regression analysis, skilled analysts can minimize those risks. And considering the impact of multiple variables at once is one of the biggest advantages of regression.

How do companies use it?

Regression analysis is the “go-to method in analytics,” says Redman. And smart companies use it to make decisions about all sorts of business issues. “As managers, we want to figure out how we can impact sales or employee retention or recruiting the best people. It helps us figure out what we can do.”

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Most companies use regression analysis to explain a phenomenon they want to understand (e.g. why did customer service calls drop last month?); predict things about the future (e.g. what will sales look like over the next six months?); or to decide what to do (e.g. should we go with this promotion or a different one?).

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A note about “correlation is not causation”

Whenever you work with regression analysis or any other analysis that tries to explain the impact of one factor on another, you need to remember the important adage: Correlation is not causation. This is critical and here’s why: It’s easy to say that there is a correlation between rain and monthly sales. The regression shows that they are indeed related. But it’s an entirely different thing to say that rain caused the sales. Unless you’re selling umbrellas, it might be difficult to prove that there is cause and effect.

Sometimes factors are correlated that are so obviously not connected by cause and effect but more often in business, it’s not so obvious. When you see a correlation from a regression analysis, you can’t make assumptions, says Redman. Instead, “You have to go out and see what’s happening in the real world. What’s the physical mechanism that’s causing the relationship?” Go out an observe consumers buying your product in the rain, talk to them, and find out, what is actually causing them to make the purchase. “A lot of people skip this step and I think it’s because they’re lazy. The goal is not to figure out what is going on in the data but to figure out is what is going on in the world. You have to go out and pound the pavement,” he says.

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Redman wrote about his own experiment and analysis in trying to lose weight and the connection between his travel and weight gain. He noticed that when he traveled, he ate more and exercised less. So was his weight gain caused by travel? Not necessarily. “It was nice to quantify what was happening but travel isn’t the cause. It may be related,” he says, but it’s not like his being on the road put those extra pounds on. He had to understand more about what was happening during his trips. “I’m often in new environments so maybe I’m eating more because I’m nervous?” He needed to look more closely at the correlation. And this is his advice to managers. Use the data to guide more experiments, not to make conclusions about cause and effect.

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What mistakes do people make when working with regression analysis?

As a consumer of regression analysis, there are several things you need to keep in mind.

First, don’t tell your data analyst to go out and figure out what is affecting sales. “The way most analyses go haywire is the manager hasn’t narrowed the focus on what he or she is looking for,” says Redman. It’s your job to identify the factors that you suspect are having an impact and ask your analyst to look at those. “If you tell a data scientist to go on a fishing expedition, or to tell you something you don’t know, then you deserve what you get, which is bad analysis,” he says. In other words, don’t ask your analysts to look at every variable they can possibly get their hands on all at once. If you do, you’re likely to find relationships that don’t really exist. It’s the same principle as flipping a coin: do it enough times, you’ll eventually think you see something interesting, like a bunch of heads all in a row.

Also keep in mind whether or not you can do anything about the independent variable you’re considering. You can’t change how much it rains so how important is it to understand that? “We can’t do anything about weather or our competitor’s promotion but we can affect our own promotions or add features, for example,” says Redman. Always ask yourself what you will do with the data. What actions will you take? What decisions will you make?

Second, “analyses are very sensitive to bad data” so be careful about the data you collect and how you collect it, and know whether you can trust it. “All the data doesn’t have to be correct or perfect,” explains Redman but consider what you will be doing with the analysis. If the decisions you’ll make as a result don’t have a huge impact on your business, then it’s OK if the data is “kind of leaky.” But “if you’re trying to decide whether to build 8 or 10 of something and each one costs $1 million to build, then it’s a bigger deal,” he says. The chart below explains how to think about whether to act on the data.

Redman says that some managers who are new to understanding regression analysis make the mistake of ignoring the error term. This is dangerous because they’re making the relationship between something more certain than it is. “Oftentimes the results spit out of a computer and managers think, ‘That’s great, let’s use this going forward.’” But remember that the results are always uncertain. As Redman points out, “If the regression explains 90% of the relationship, that’s great. But if it explains 10%, and you act like it’s 90%, that’s not good.” The point of the analysis is to quantify the certainty that something will happen. “It’s not telling you how rain will influence your sales, but it’s telling you the probability that rain may influence your sales.”

The last mistake that Redman warns against is letting data replace your intuition.

“You always have to lay your intuition on top of the data,” he explains. Ask yourself whether the results fit with your understanding of the situation. And if you see something that doesn’t make sense ask whether the data was right or whether there is indeed a large error term. Redman suggests you look to more experienced managers or other analyses if you’re getting something that doesn’t make sense. And, he says, never forget to look beyond the numbers to what’s happening outside your office: “You need to pair any analysis with study of real world. The best scientists — and managers — look at both.”

You can move beyond the visual regression analysis that the scatter plot technique provides. You can use Excel’s Regression tool provided by the Data Analysis add-in. For example, say that you used the scatter plotting technique, to begin looking at a simple data set. You can then create a scatterplot in excel. And, after that initial examination, suppose that you want to look more closely at the data by using full blown, take-no-prisoners, regression.

To perform regression analysis by using the Data Analysis add-in, do the following:

1. Tell Excel that you want to join the big leagues by clicking the Data Analysis command button on the Data tab.

2. When Excel displays the Data Analysis dialog box, select the Regression tool from the Analysis Tools list and then click OK.

   Excel displays the Regression dialog box.

3. Identify your Y and X values.

   Use the Input Y Range text box to identify the worksheet range holding your dependent variables. Then use the Input X Range text box to identify the worksheet range reference holding your independent variables.

   Each of these input ranges must be a single column of values. For example, if you want to use the Regression tool to explore the effect of advertisements on sales, you enter $A$1:$A$11 into the Input X Range text box and $B$1:$B$11 into the Input Y Range text box. If your input ranges include a label, select the Labels check box.

4. (Optional) Set the constant to zero.

   If the regression line should start at zero — in other words, if the dependent value should equal zero when the independent value equals zero — select the Constant Is Zero check box.

5. (Optional) Calculate a confidence level in your regression analysis.

   To do this, select the Confidence Level check box and then (in the Confidence Level text box) enter the confidence level you want to use.

6. Select a location for the regression analysis results.

   Use the Output Options radio buttons and text boxes to specify where Excel should place the results of the regression analysis. To place the regression results into a range in the existing worksheet, for example, select the Output Range radio button and then identify the range address in the Output Range text box. To place the regression results someplace else, select one of the other option radio buttons.

7. Identify what data you want returned.

   Select from the Residuals check boxes to specify what residuals results you want returned as part of the regression analysis.

   Similarly, select the Normal Probability Plots check box to add residuals and normal probability information to the regression analysis results.

8. Click OK.

   Excel shows a portion of the regression analysis results including three, stacked visual plots of data from the regression analysis.

   There is a range that supplies some basic regression statistics, including the R-square value, the standard error, and the number of observations. Below that information, the Regression tool supplies analysis of variance (or ANOVA) data, including information about the degrees of freedom, sum-of-squares value, mean square value, the f-value, and the significance of F.

   Beneath the ANOVA information, the Regression tool supplies information about the regression line calculated from the data, including the coefficient, standard error, t-stat, and probability values for the intercept — as well as the same information for the independent variable, which is the number of ads. Excel also plots out some of the regression data using simple scatter charts.