![]() ![]() While you will get P values for the null hypotheses, you should use them as a guide to building a multiple regression equation you should not use the P values as a test of biological null hypotheses about whether a particular X variable causes variation in Y. As you are doing a multiple regression, you'll also test a null hypothesis for each X variable, that adding that X variable to the multiple regression does not improve the fit of the multiple regression equation any more than expected by chance. The main null hypothesis of a multiple regression is that there is no relationship between the X variables and the Y variable in other words, the Y values you predict from your multiple regression equation are no closer to the actual Y values than you would expect by chance. It's very easy to get misled by the results of a fancy multiple regression analysis, and you should use the results more as a suggestion, rather than for hypothesis testing. I'll say this more than once on this page: you have to be very careful if you're going to try to use multiple regression to understand cause-and-effect relationships. Multiple regression is a statistical way to try to control for this it can answer questions like "If sand particle size (and every other measured variable) were the same, would the regression of beetle density on wave exposure be significant?" Maybe sand particle size is really important, and the correlation between it and wave exposure is the only reason for a significant regression between wave exposure and beetle density. However, sand particle size and wave exposure are correlated beaches with bigger waves tend to have bigger sand particles. If you did a regression of tiger beetle density on wave exposure by itself, you would probably see a significant relationship. For example, if you did a regression of tiger beetle density on sand particle size by itself, you would probably see a significant relationship. Multiple regression for understanding causesĪ second use of multiple regression is to try to understand the functional relationships between the dependent and independent variables, to try to see what might be causing the variation in the dependent variable. This could help you guide your conservation efforts, so you don't waste resources introducing tiger beetles to beaches that won't support very many of them. Then if you went to a beach that doesn't have tiger beetles and measured all the independent variables (wave exposure, sand particle size, etc.) you could use your multiple regression equation to predict the density of tiger beetles that could live there if you introduced them. Multiple regression would give you an equation that would relate the tiger beetle density to a function of all the other variables. You've gone to a number of beaches that already have the beetles and measured the density of tiger beetles (the dependent variable) and several biotic and abiotic factors, such as wave exposure, sand particle size, beach steepness, density of amphipods and other prey organisms, etc. For example, let's say you're interested in finding suitable habitat to reintroduce the rare beach tiger beetle, Cicindela dorsalis dorsalis, which lives on sandy beaches on the Atlantic coast of North America. One use of multiple regression is prediction or estimation of an unknown Y value corresponding to a set of X values. Multiple regression for prediction Atlantic beach tiger beetle, Cicindela dorsalis dorsalis. The purpose of a multiple regression is to find an equation that best predicts the Y variable as a linear function of the X variables. The rest of the variables are the independent ( X) variables you think they may have an effect on the dependent variable. One of the measurement variables is the dependent ( Y) variable. Use multiple regression when you have three or more measurement variables. You can use it to predict values of the dependent variable, or if you're careful, you can use it for suggestions about which independent variables have a major effect on the dependent variable. Use multiple regression when you have a more than two measurement variables, one is the dependent variable and the rest are independent variables. ![]()
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