Learn about simple regression analysis.
- [Instructor] Let's talk about regression analysis. You might not be familiar with the term, but a regression analysis is a very powerful business tool that you can use to make predictions and forecasts for your firm. In particular, a regression is simply a statistical model. In it's most basic form, a regression is defined by the equation you see here, y = ax + b. What this is simply saying is that our dependent variable y is driven by our independent variable x plus a y intercept b.
So we might think about this in say, a situation trying to figure out how long it'll take to drive to California from somewhere else in the country. The time to reach California is going to be based on two factors, how fast we're traveling and where we start from. A is the speed at which we're driving. X is the number of hours it'll take us to reach California. And b is where we start from. It takes longer to reach California starting from Virginia, for example, than it does if we start from Colorado.
Similarly, it'll take us less time to reach California if we're driving 100 miles per hour versus if we're driving 10 miles per hour. Y = ax + b can help us to predict how long that trip will take. We can use this same concept to make predictions in business as well. This picture, showing the dependent variable y against the independent variable x illustrates using a regression based on a bunch of data points.
For example, we might think about multiple car trips having been made from different points at different places in the country and at different speeds. That line, the red line shown here, essentially helps us to predict how long it takes to get from a particular place in the country to California based on the speed at which we're driving, x. We gather data on multiple different car trips that were made, and we could put them onto a graph like this and then fit that line to it.
That line is called a regression line. This is referred to as a simple regression, we're fitting a straight line to our data and it lets us predict the dependent variable y based on the value of our independent variables in x. Now obviously, in business, most predictions that we're going to make are driven by a lot more than one variable. Unlike when driving a car, in business there are many things that could impact say, our sales. The business environment, the number of sales people we have, the amount we spend on marketing, it's easy to think of 10 or 20 different factors.
Well we can incorporate all of these into one larger model which we refer to as a multiple regression. This picture illustrates using a multiple regression to try and fit an equation or a predictive model to a slew of different data. As you can see, there is a curved pattern in this data. Our multiple regression allows us to go through and look at all of the data and make predictions based on it.
Now regressions aren't perfect, but they do give us a way to map to harness mounds of data that are out there. And hence they're very powerful in business. Let's take a look at an example of what regression output looks like. This is raw output for a regression. This is going to show us, in essence, what our data looks like once it's run through software and gives us a predictive output. In the first row, you'll see culture here.
Culture, in this case, refers to the sales culture of the firm. Our coefficient 1.57 shows us that when we spend $1 on sales training, we get an additional $1.57 in sales as a result. All of these other variables below it, tdebt, capexta, et cetera refer to things like total debt, capital expenditures to total assets, they're characteristics of the firm. Overall then, our goal is to take this mass of data and look at just one variable that we care about.
Whether spending additional money on training our sales team provides additional sales results. This regression gives us a point estimate for that investment. We get $1.57 of additional sales for every $1 that we spent on training our sales team. This is an example of how we can use the power of regression to make relevant predictions for our firm.
Professor Michael McDonald demonstrates how to harness the wealth of information available on the Internet to forecast statistics such as industry growth, GDP, and unemployment rates, as well as factors that directly affect your business, like property prices and future interest rate hikes. All you need is Microsoft Excel. Michael uses the built-in formulas, functions, and calculations to perform regression analysis, calculate confidence intervals, and stress test your results. He also covers time series exponential smoothing, fixed effects regression, and difference estimators. You'll walk away from the course able to immediately begin creating forecasts for your own business needs.
- Understanding big data and economic forecasting
- Predicting values with regressions
- Analyzing economic trends and economic cycles
- Using fixed-effects regressions and binary regressions for forecasting
- Assessing the accuracy of an economic forecast
- Using scenario analysis