If I'm doing a pearson's and need to know the percentage of predicitability...
all I have to do is work out the pearon's, right?
To clarify, if you are referring to the coefficient of determination, also known as the percentage of predictability or R-squared value, then it cannot be directly obtained by calculating Pearson's correlation coefficient. To calculate the percentage of predictability in a linear regression model, you need to follow these steps:
1. Perform linear regression: Start by fitting a linear regression model to your data. This involves finding the best-fit line that represents the relationship between the independent and dependent variables.
2. Calculate the total sum of squares (SST): SST measures the total variation in the dependent variable. It is calculated by summing up the squared differences between each actual dependent variable value and the mean of the dependent variable.
3. Calculate the sum of squared errors (SSE): SSE measures the unexplained variation in the dependent variable that is left after fitting the regression line. It is calculated by summing up the squared differences between each actual dependent variable value and the corresponding predicted value from the regression line.
4. Calculate the coefficient of determination (R-squared): R-squared represents the proportion of the dependent variable's variation that can be explained by the independent variable(s). It is calculated by subtracting the ratio of SSE to SST from 1:
R-squared = 1 - (SSE / SST)
5. Convert R-squared to a percentage: If desired, you can multiply the R-squared value by 100 to express it as a percentage. This percentage quantifies the predictability of the dependent variable using the independent variable(s) incorporated in the model.
So, in summary, to obtain the percentage of predictability or R-squared value, you need to perform linear regression and calculate the ratio of the sum of squared errors (SSE) to the total sum of squares (SST), and then convert it to a percentage by multiplying by 100 if desired.