1. Regression Basics For Business Analysis If you've ever wondered how two or more things relate to each other, or if you've ever had your boss ask you to create a forecast or analyze relationships between variables, then learning regression would be worth your time. In this article, you'll learn the basics of simple linear regression - a tool commonly used in forecasting and financial analysis. We will begin by learning the core principles of regression, first learning about covariance and correlation, and then move on to building and interpreting a regression output. A lot of software such as Microsoft Excel can do all the regression calculations and outputs for you, but it is still important to learn the underlying mechanics.regressioncovariancecorrelation

2. Variables At the center of regression is the relationship between two variables, called the dependent and independent variables. For instance, suppose you want to forecast sales for your company and you've concluded that your company's sales go up and down depending on changes in GDP.GDP Covariance The formula to calculate the relationship between two variables is called covariance. This calculation shows you the direction of the relationship as well as its relative strength.relationship between two variables is called covariance

3. Correlation Coefficient We need to standardize the covariance in order to allow us to better interpret and use it in forecasting, and the result is the correlation calculation.the result is the correlation calculation The correlation calculation simply takes the covariance and divides it by the product of the standard deviation of the two variables. This will bound the correlation between a value of -1 and +1.standard deviation

4. Regression Equation Now that we know how the relative relationship between the two variables is calculated, we can develop a regression equation to forecast or predict the variable we desire. Below is the formula for a simple linear regression. The "y" is the value we are trying to forecast, the "b" is the slope of the regression, the "x" is the value of our independent value, and the "a" represents the y-intercept. The regression equation simply describes the relationship between the dependent variable (y) and the independent variable (x). The intercept, or "a", is the value of y (dependent variable) if the value of x (independent variable) is zero. So if there was no change in GDP, your company would still make some sales - this value, when the change in GDP is zero, is the intercept.

5. Linear regression attempts to estimate a line that best fits the data, and the equation of that line results in the regression equation. Excel Now that you understand some of the background that goes into regression analysis, let's do a simple example using Excel's regression tools. We'll build on the previous example of trying to forecast next year's sales based on changes in GDP. The next table lists some artificial data points, but these numbers can be easily accessible in real life. YearSalesGDP 20051001.00% 20062501.90% 20072752.40% 20082002.60% 20093002.90%

6. Just eyeballing the table, you can see that there is going to be a positive correlation between sales and GDP. Both tend to go up together. Using Excel, all you have to do is click the Tools drop-down menu, select Data Analysis, and from there choose Regression.Using Excel, all you have to do The popup box is easy to fill in from there; your Input Y Range is your "Sales" column and your Input X Range is the change in GDP column; choose the output range for where you want the data to show up on your spreadsheet and press OK. You should see something similar to what is given in the table below Regression StatisticsCoefficients Multiple R0.8292243Intercept34.58409 R Square0.687613GDP88.15552 Adjusted R Square0.583484-- Standard Error51.021807-- Observations5--

7. Interpretation The major outputs you need to be concerned about for simple linear regression are the R-squared, the intercept and the GDP coefficient.R-squared The R-squared number in this example is 68.7% - this shows how well our model predicts or forecasts the future sales. Next we have an intercept of 34.58, which tells us that if the change in GDP was forecasted to be zero, our sales would be about 35 units. And lastly, the GDP correlation coefficient of 88.15 tells us that if GDP increases by 1%, sales will likely go up by about 88 units. So how would you use this simple model in your business? Well if your research leads you to believe that the next GDP change will be a certain percentage, you can plug that percentage into the model and generate a sales forecast. This can help you develop a more objective plan and budget for the upcoming year.

8. EXERCISE In this case, you would plot last year's data for monthly sales and advertising expenditures as shown on the scatter plot below. (Data for independent and dependent variables must be from the same period of time.)

9. Did you get this? Scatter plots are effective in visually identifying relationships between variables. These relationships can be expressed mathematically in terms of a correlation coefficient, which is commonly referred to as a correlation.

10. Regression Line – May you try? The figure below is the same as the scatter plot above, with the addition of a regression line fitted to the historical data. The regression line is the line with the smallest possible set of distances between itself and each data point. As you can see, the regression line touches some data points, but not others. The distances of the data points from the regression line are called error terms.

11. Regression analysis – Excel Formula You use the LINEST function to perform a regression analysis.LINEST function And you perform a regression analysis when you need to know, for example, how an athlete's performance is affected by age, height, and weight. You can then use the results to predict the performance of a new, untested athlete. In other words, you're estimating likelihood. As an example, say you have sales data from January to June, and you want to predict sales for September. You'd use the LINEST function like this:

12. Remember to enter LINEST as an array formulaan array formula (press Ctrl+Shift+Enter instead of just Enter).

13. Give it a try The sample data shown here uses the LINEST function to estimate future sales. This Excel Online workbook shows the LINEST function being used with SUM in an array formula. Copy all the cells in the table below and paste them into cell A1 in a new worksheet in Excel. Then, select cell B9 and press Ctrl+Shift+Enter to enter it as an array formula. The result in B9 should be 11,000. MonthSales 1$3,100 2$4,500 3$4,400 4$5,400 5$7,500 6$8,100 Formula =SUM(LINEST(B1:B6, A1:A6)*{9,1})