An exponential function is a mathematical function where the independent variable (usually denoted as x) is an exponent. It can be written in the form y = ab^x, where a and b are constants and b is the base of the exponential function.
To calculate R Square of an exponential function, you first need to fit the data points to the exponential function using a regression analysis tool. Once the curve is fitted, you can use the formula R^2 = 1 - (SSres/SStot), where SSres is the sum of squares of residuals and SStot is the total sum of squares. This will give you the R Square value, which represents the goodness of fit of the exponential function to the data.
R Square is a statistical measure that represents the proportion of variation in the dependent variable (y) that can be explained by the independent variable (x). In the case of an exponential function, a high R Square value indicates that the curve fits well to the data points and the relationship between x and y is strong. On the other hand, a low R Square value indicates a poor fit and a weak relationship between x and y.
No, R Square cannot be negative for an exponential function. Since R Square is calculated as the square of the correlation coefficient (r), which ranges from -1 to 1, the R Square value will always be between 0 and 1 for an exponential function. A negative value of r indicates a negative correlation between x and y, but when squared, it becomes positive and thus the R Square cannot be negative.
R Square can be used to compare the goodness of fit of different exponential functions to the same set of data points. A higher R Square value indicates a better fit and a stronger relationship between x and y, while a lower R Square value indicates a weaker fit. However, it is important to note that R Square should not be the only factor considered when comparing different models, as it can be influenced by the number of data points and the complexity of the model.