Category: Linear regression. The linear regression model provides a framework for quantitative predictions of an outcome variable that is continuous, using one or more predictor variables. Articles are arranged by date with the most recent entries at the top. You can find the theme and closely related categories and other resources at the bottom of this page.

Stats: What statistic should I use when? (January 4, 2008). Someone was asking about a multiple choice question on a test that reads something like this: A group of researchers investigating in patients with diabetes on the basis of demographic characteristics and the level of diabetic control. Select the most appropriate statistical method to use in analyzing the data: a t-test, ANOVA, multiple linear regression, or a chi-square test. This is one of the more vexing things that people face--what statistic should I use when.

Stats: Accounting for cyclical trends in a regression model (June 13, 2007). One of the doctors brought by a data set that showed the average volume of business (number of beds filled) in a month for 28 consecutive months starting in January 2005. The number of beds filled is highest in the wintertime and lowest in the summertime. Also there is slight upward trend over time. If you were trying to estimate the magnitude of this slight upward trend, you would need to account for the cyclical pattern as well. A simple way to estimate a cyclical pattern is to use a bit of trigonometry.

Stats: Tests of hypothesis and confidence intervals involving a correlation coefficient (January 18, 2007). Suppose you compute a correlation coefficient from a sample of patients. Can you test a hypothesis about this correlation? Can you place confidence limits around this correlation? Yes, you can, but there are a wide array of approaches that you could use.

Stats: Fitting a quadratic regression model (November 15, 2006). Someone came in asking about how to examine for non-linear relationships among variables. In particular, they wanted to look for a U-shaped pattern where a little bit of something was better than nothing at all, but too much of it might backfire and be as bad as nothing at all. The simplest way, but not necessarily the best way, to examine for a nonlinear relationship is to fit a quadratic model, but when I told this person about quadratic regression, I just got a blank stare. So I thought it would be nice to show how this is done in SPSS.

Stats: An amusing correlation (June 5, 2006). I always like simple amusing examples that illustrate an important statistical point. An email by JW on EDSTAT-L offer a couple of examples.

Stats: Interpretation of the correlation coefficient (April 4, 2006). There are many "rules of thumb" about how to interpret a correlation coefficient. They vary slightly from one to another, but all say about the same thing. Here's a couple of interpretations I found on the web today:

Stats: Can you use the coefficient of determination for categorical variables (April 4, 2006). Dear Professor Mean, How can you compute a coefficient of determination (R squared) for a model that has a dichotomous variable? I thought that you could only compute this in a linear regression model?

Stats: What is a beta coefficient? (April 4, 2006). When you are examining the relative impact of several independent variables on an outcome variable, the estimated slopes may be deceptive. A variable with a wide range might have a very flat slope compared to a variable with a large range, even though the former may be a much more powerful predictor. You can see this intuitively by drawing a graph with a large aspect ratio (much wider than it is tall) and comparing it with the same graph with a smaller aspect ratio (closer to square). The slope looks so much bigger in the square graph, but nothing has fundamentally changed. The statistics community has developed "beta coefficients" that are the regression coefficients using a standardized variables. When you standardize, you allow for a "fair" comparison of the predictive power of variables measured on disparate ranges or even expressed in noncomparable units of measurement.

Stats: Economic evaluations (February 2, 2006). Several years ago, BMJ had a whole series of articles on economic evaluations. I saved the references at the time, and am just now getting back to review them. There are a lot of important lessons in these articles, and like all articles in BMJ (except for their most recent 12 months of publications), the full free text is available on the web.

Stats: Interpreting linear regression coefficients (June 24, 2002). In linear regression, we use a straight linear to estimate a trend in data. We can't always draw a straight line that passes through every data point, but we can find a line that "comes close" to most of the data. This line is an estimate, and we interpret the slope and the intercept of this line as follows.

Stats: Exploring interactions in a linear regression model (August 1, 2002). Dear Professor Mean, I have a model with two factors. When I ran the model, it showed a significant interaction between the two factors. What do I do now? --Troubled Trudy

Stats: SPSS dialog boxes for linear model examples (June 21, 2002). This handout will show the SPSS dialog boxes that I used to create linar regression examples. I will capitalize variable names, field names and menu picks for clarity.

Stats: Regression to the mean (January 27, 2000). Dear Professor Mean: In a stat course, I was introduced to the term "regression to the mean". Today we administered a pretest to 4th graders. In February we will test again, with the same exam, to see "how much they've learned". I explained to the principal that, of course they would do better, no matter how well they were taught, that this was a classic case of regression to the mean. Am I correct, close, or way off on this?

Stats: Guidelines for linear regression models (September 21, 1999). Linear regression models provide a good way to examine how various factors influence a continuous outcome measure. There are three steps in a typical linear regression analysis. 1. Fit a crude model, 2. Fit an adjusted model, 3. Analyze predicted values and residuals. These steps may not be appropriate for every linear regression analysis, but they do serve as a general guideline. In this presentation, you will see these steps applied to data from a breast feeding study, using SPSS software.

Stats: R-squared (August 18, 1999). Dear Professor Mean, On my TI-83, when calculating quadratic regression, there is a number that is found called R-squared (R^2). I understand that this is the coefficient of determination. But....I thought that R^2 had to do with linear models. What is R^2 finding for this quadratic regression? what does this number mean? is there a way to find R^2 through a "pencil and paper" process?? I know the equation for R^2 for a linear regression. But its the quadratic I need to know about. please, anyone, help!!

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Creative Commons License This work is licensed under a Creative Commons Attribution 3.0 United States License. It was written by Steve Simon on 2007-06-13, edited by Steve Simon, and was last modified on 2008-01-28. Send feedback to ssimon at cmh dot edu or click on the email link at the top of the page.