When do i use regression

If X is our increase in ticket price, this informs us that if there is no increase in ticket price, event satisfaction will still increase by points. Regression lines always consider an error term because in reality, independent variables are never precisely perfect predictors of dependent variables. This makes sense while looking at the impact of ticket prices on event satisfaction — there are clearly other variables that are contributing to event satisfaction outside of price.

Your regression line is simply an estimate based on the data available to you. So, the larger your error term, the less definitively certain your regression line is. Regression analysis is helpful statistical method that can be leveraged across an organization to determine the degree to which particular independent variables are influencing dependent variables. The possible scenarios for conducting regression analysis to yield valuable, actionable business insights are endless.

The next time someone in your business is proposing a hypothesis that states that one factor, whether you can control that factor or not, is impacting a portion of the business, suggest performing a regression analysis to determine just how confident you should be in that hypothesis! This will allow you to make more informed business decisions, allocate resources more efficiently, and ultimately boost your bottom line.

We use cookies to track how our visitors are browsing and engaging with our website in order to understand and improve the user experience. Review our Privacy Policy to learn more. Regression analysis provides detailed insight that can be applied to further improve products and services.

The beta-weights [5] of the explanatory variables can be compared to answer this question. Dive down for a discussion of the distinction between t-ratios and beta-weights. Example: In the full model, the beta-weight of mileage is roughly twice that of age, which in turn is more than twice that of make. Of secondary explanatory importance is that they vary in age. Trailing both is the fact that some are Fords and others Hondas, i. Some interesting relationships are linear, essentially all managerial relationships are at least locally linear, and several modeling tricks help to transform the most commonly-encountered nonlinear relationships into linear relationships.

Given the choice, use the one with the adjective. It is the magnitude, i. Which can we ignore? How do those factors interact with each other?

And, perhaps most importantly, how certain are we about all of these factors? In regression analysis, those factors are called variables. And then you have your independent variables — the factors you suspect have an impact on your dependent variable. In order to conduct a regression analysis, you gather the data on the variables in question. Then you plot all of that information on a chart that looks like this:.

Glancing at this data, you probably notice that sales are higher on days when it rains a lot. 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. 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. Just focus on the model:. And in the past, for every additional inch of rain, you made an average of five more sales.

If there are not too much missing data, and there does not seem to be any pattern in terms of what is missing, then you don't really need to worry. Just run your regression, and any cases that do not have values for the variables used in that regression will not be included. Although tempting, do not assume that there is no pattern; check for this. To do this, separate the dataset into two groups: those cases missing values for a certain variable, and those not missing a value for that variable.

Using t-tests, you can determine if the two groups differ on other variables included in the sample. For example, you might find that the cases that are missing values for the "salary" variable are younger than those cases that have values for salary. You would want to do t-tests for each variable with a lot of missing values.

If there is a systematic difference between the two groups i. After examining your data, you may decide that you want to replace the missing values with some other value. The easiest thing to use as the replacement value is the mean of this variable. Some statistics programs have an option within regression where you can replace the missing value with the mean. Alternatively, you may want to substitute a group mean e. The default option of statistics packages is to exclude cases that are missing values for any variable that is included in regression.

But that case could be included in another regression, as long as it was not missing values on any of the variables included in that analysis. You can change this option so that your regression analysis does not exclude cases that are missing data for any variable included in the regression, but then you might have a different number of cases for each variable.

Outliers You also need to check your data for outliers i. If you feel that the cases that produced the outliers are not part of the same "population" as the other cases, then you might just want to delete those cases. Alternatively, you might want to count those extreme values as "missing," but retain the case for other variables. Alternatively, you could retain the outlier, but reduce how extreme it is.

Specifically, you might want to recode the value so that it is the highest or lowest non-outlier value. Normality You also want to check that your data is normally distributed.

To do this, you can construct histograms and "look" at the data to see its distribution. Often the histogram will include a line that depicts what the shape would look like if the distribution were truly normal and you can "eyeball" how much the actual distribution deviates from this line.

This histogram shows that age is normally distributed: You can also construct a normal probability plot. In this plot, the actual scores are ranked and sorted, and an expected normal value is computed and compared with an actual normal value for each case.

The expected normal value is the position a case with that rank holds in a normal distribution. The normal value is the position it holds in the actual distribution. Basically, you would like to see your actual values lining up along the diagonal that goes from lower left to upper right. This plot also shows that age is normally distributed: You can also test for normality within the regression analysis by looking at a plot of the "residuals.

Residuals will be explained in more detail in a later section. If the data are normally distributed, then residuals should be normally distributed around each predicted DV score. If the data and the residuals are normally distributed, the residuals scatterplot will show the majority of residuals at the center of the plot for each value of the predicted score, with some residuals trailing off symmetrically from the center.

You might want to do the residual plot before graphing each variable separately because if this residuals plot looks good, then you don't need to do the separate plots. Below is a residual plot of a regression where age of patient and time in months since diagnosis are used to predict breast tumor size. These data are not perfectly normally distributed in that the residuals about the zero line appear slightly more spread out than those below the zero line.

Nevertheless, they do appear to be fairly normally distributed. In addition to a graphic examination of the data, you can also statistically examine the data's normality. Specifically, statistical programs such as SPSS will calculate the skewness and kurtosis for each variable; an extreme value for either one would tell you that the data are not normally distributed.

If any variable is not normally distributed, then you will probably want to transform it which will be discussed in a later section. Checking for outliers will also help with the normality problem.

Linearity Regression analysis also has an assumption of linearity. Linearity means that there is a straight line relationship between the IVs and the DV. This assumption is important because regression analysis only tests for a linear relationship between the IVs and the DV.

Any nonlinear relationship between the IV and DV is ignored. You can test for linearity between an IV and the DV by looking at a bivariate scatterplot i. If the two variables are linearly related, the scatterplot will be oval. Looking at the above bivariate scatterplot, you can see that friends is linearly related to happiness.