We can also see the relationship between x and y by creating a scatter chart for the original data and choosing Layout > Analysis|Trendline in Excel and then selecting the Power Trendline option (after choosing More Trendline Options). We now use the Regression data analysis tool to model the relationship between ln y and ln x.įigure 2 – Log-log regression model for Example 1įigure 2 shows that the model is a good fit and the relationship between ln x and ln y is given byĪpplying e to both sides of the equation yields The table on the right side of Figure 1 shows y transformed into ln y and x transformed into ln x. It follows that any such model can be expressed as a power regression model of form y = αx βby setting α = e δ.Įxample 1: Determine whether the data on the left side of Figure 1 is a good fit for a power model.įigure 1 – Data for Example 1 and log-log transformation This equation has the form of a linear regression model (where I have added an error term ε):Ī model of the form ln y = β ln x + δ is referred to as a log-log regression model. Taking the natural log (see Exponentials and Logs) of both sides of the equation, we have the following equivalent equation: Another non-linear regression model is the power regression model, which is based on the following equation:
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