Statistics

In my previous post, I explained What logistic regression is and also explained odds, odds ratio and model equation. Today, I’ll introduce Firth’s Logistic Regression. Common logistic regression is mostly used when the sample size is sufficiently large, and the outcome variable (0 and 1) is well-balanced. Also, it is used when there is no … Read more

When performing a t-test, a confidence interval can be obtained. Below, I describe how to calculate the confidence interval manually, step by step. 1) Difference in means 2) Pooled variance 3) Standard error 4) Degrees of freedom 5) Confidence interval and let’s calculate the confidence interval We aim to develop open-source code for agronomy ([email protected]) … Read more

Recently, I’ve been focusing on Bayesian statistics. To organize the concepts for myself as well, I’m going to explain Bayes’ theorem as simply as possible. Let’s import a dataset from Kaggle. https://www.kaggle.com/datasets/cameronseamons/electronic-sales-sep2023-sep2024 This dataset contains information used to analyze customer purchasing behavior at an electronics store. You can download it from Kaggle after creating an … Read more

The Gamma distribution is a flexible family of continuous probability distributions defined only for non-negative values (x>0). It’s commonly used to model quantities that represent time, size, or waiting periods—anything that can’t go below zero and often shows right-skewed behavior (a long tail toward larger values). In essence, the Gamma distribution describes how likely different … Read more

In my previous post, I suggested different statistical models for agrivoltaics studies to explain why we should consider Linear Mixed Models in this field. In many agrivoltaics studies, researchers overlook the actual experimental layout and analyze data using split-plot or RCBD models, focusing only on treatment variables (e.g., inside vs. outside the solar panel array). … Read more

□ Quantifying Phenotypic Plasticity of Crops In my previous post, I explained how to quantify phenotypic plasticity in crops and described three different approaches: 1) Responsiveness, 2) Reaction Norm, and the 3) Finlay-Wilkinson Regression Model. Responsiveness is calculated as (Treatment − Control) / Control. It indicates how the dependent variable (e.g., yield) responds to a … Read more

In my previous post, I explained how to calculate the Log-Likelihood, AIC, and BIC in a regression model. In this post, I will demonstrate the same concepts, but in the context of an ANOVA model. Here I have one dataset. Let’s say this data represents yield in response to different fertilizer types (Control, Slow, and … Read more

Here I have one dataset. I want to predict grain weight using grain dimension data such as length, width, and area, and identify the best prediction model for estimating grain weight. As a result, I developed the following models. and I’ll calculate Log-likelihood for each model. To do that, I need to know each model … Read more

Principal Component Analysis (PCA) is a statistical technique used for dimensionality reduction while preserving as much variability in the data as possible. It transforms the original variables in a dataset into a new set of uncorrelated variables called principal components, ordered by the amount of variance they capture from the original dataset. Here’s the step … Read more

Mean Absolute Error (MAE) is a metric used to measure the accuracy of a model’s predictions. It calculates the average magnitude of the errors in a set of predictions, without considering their direction. In other words, MAE measures the average absolute difference between the actual values and the predicted values. MAE is typically used in … Read more

□ Understanding Multiple Linear Regression Easily (Part 1: Calculating the Regression Equation Manually) In the previous post, we explained how to manually calculate the regression equation in multiple linear regression analysis. Now, in this post, I will explain how to calculate the coefficient of determination (R2) in multiple linear regression analysis. No. Yield (yi) Time … Read more

In my previous posts, I explained the simple linear regression model as five categories. I recommend reading the following posts first. □ Simple linear regression (1/5)- correlation and covariance□ Simple linear regression (2/5)- slope and intercept of linear regression model□ Simple linear regression (3/5)- standard error of slope and intercept□ Simple linear regression (4/5)- t … Read more

Today, I’ll try to explain factorial experiments in the simplest way. When you apply multiple different factors simultaneously to derive experimental results, it’s called factorial experiments. The different treatments within the experiment are referred to as ‘factorials.’ In other words, a factorial is a combination of factors. [Note 1] A factorial experiment is a research … Read more

Here is data for x and y. I would like to perform regression analysis to understand how y changes with x. n x y 1 10 30 2 20 40 3 30 50 4 40 80 5 50 90 6 60 100 7 70 120 I have data for x and y as described above, … Read more