Your third option is curvilinear regression: finding an equation that produces a curved line that fits your points. The second null hypothesis of curvilinear regression is that the increase in \(R^2\) is only as large as you would expect by chance. A cubic equation will always have a higher \(R^2\) than quadratic, and so on. So the quadratic equation will always have a higher \(R^2\) than the linear. Will always be closer to the points than a linear equation of the form As you add more parameters to an equation, it will always fit the data better for example, a quadratic equation of the form You measure the fit of an equation to the data with \(R^2\), analogous to the \(r^2\) of linear regression. This is analogous to testing the null hypothesis that the slope is \(0\) in a linear regression. One null hypothesis you can test when doing curvilinear regression is that there is no relationship between the \(X\) and \(Y\) variables in other words, that knowing the value of \(X\) would not help you predict the value of \(Y\). And if you want to use the regression equation for prediction or you're interested in the strength of the relationship (\(r^2\)), you should definitely not use linear regression and correlation when the relationship is curved. However, it will look strange if you use linear regression and correlation on a relationship that is strongly curved, and some curved relationships, such as a U-shape, can give a non-significant \(P\) value even when the fit to a U-shaped curve is quite good. This could be acceptable if the line is just slightly curved if your biological question is "Does more \(X\) cause more \(Y\)?", you may not care whether a straight line or a curved line fits the relationship between \(X\) and \(Y\) better. If you only want to know whether there is an association between the two variables, and you're not interested in the line that fits the points, you can use the \(P\) value from linear regression and correlation. You have three choices in this situation. In that case, the linear regression line will not be very good for describing and predicting the relationship, and the \(P\) value may not be an accurate test of the null hypothesis that the variables are not associated. Sometimes, when you analyze data with correlation and linear regression, you notice that the relationship between the independent (\(X\)) variable and dependent (\(Y\)) variable looks like it follows a curved line, not a straight line. To use curvilinear regression when you have graphed two measurement variables and you want to fit an equation for a curved line to the points on the graph.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |