The tutorial shows examples of how you can use built-in Probability Density Functions (PDF) in R, including PDF for normal distribution (dnorm), uniform distribution (dunif), and exponential distribution (dexp). Example 1: PDF for Normal Distribution Normal distribution PDF dnorm() in R returns the density of probability at 2. Note that it is standard normal distribution … Read more
This post discusses about the basic idea of probability density function, including definition and examples.
This tutorial shows how to interpret interaction effects in linear regression models. In summary, there are two perspectives, (a) mean difference perspective and (b) slope difference perspective. Interpret Interaction Effect in Linear Regression (a) Mean Difference Perspective: One way to interpret interaction effects in linear regression is based on mean differences. A significant interaction means … Read more
We can solve linear regression (i.e., estimate the regression coefficients) using just linear algebra. Below is the process of 4 steps to do regression analysis via matrix multiplication. Step 1: Prepare the matrix We actually can expand the function above to another format below. The function below can give you a more detailed idea of … Read more
This tutorial shows how to use sklearn to calculate SSR, which stands for Sum of Squared Residuals. SSR is also known as residual sum of squares (RSS) or sum of squared errors (SSE). Steps of Using sklearn to Calculate SSR in Python Step 1: Prepare data We are going to use a built-in dataset called … Read more
This tutorial shows how you calculate Sum of Squared Residuals in Python with detailed steps. Sum of Squared Residuals (SSR) is also known as residual sum of squares (RSS) or sum of squared errors (SSE). The following is the formula to calculate SSR. SSR can be used compare our estimated values and observed values for … Read more
MSR stands for Mean Squared Residuals. MSR can be used to compare the the difference between estimated Y and observed Y in model. It is ratio between Sum Squared Residuals and the number of observations, i.e., n. The following is the formula of MSR. MSR has the exact same formula as the biased MSE. How … Read more
MSE stands for Mean Squared Error. MSE is used to compare our estimated Y (DV) and observed Y in a model. This tutorial shows how you can calcuate biased and unbiased MSE in Python using 4 examples. Biased MSE and unbiased MSE The following is the formulas for biased MSE and unbiased MSE. Biased MSE … Read more
MSD stands for Mean Squared Deviation, whereas MSE stands for Mean Squared Error. Quite often, you will find that they are synonymic. Both MSD and MSE can be used to compare estimated values and observed values in a model. The key nuance is on the denominator of both MSD and MSE, as it will lead … Read more
Mean Squared Deviation (MSD) often is synonymic with Mean Squared Error (MSE). MSD can be used to compare our estimated values and observed values in a model. For MSD, there are two possible situations, unbiased MSD and biased MSD. Both of them are correct. The following are the formulas of MSD. Method 1: Unbiased MSD … Read more