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25th Sept 2023
K-fold cross-validation is a popular machine learning technique for evaluating the effectiveness of a predictive model. It entails splitting a dataset into K identically sized “folds” or subgroups. A new fold is used as the validation set each time, and the remaining K-1 folds serve as the training set. The model is then trained and validated K times. With the aid of this procedure, it is possible to make sure that the model’s performance is reliable and not unduly reliant on a certain random data split. A single performance statistic, such as accuracy or mean squared error, which gives a more accurate indication of the model’s generalization ability, is often produced by averaging the results from each iteration. K-fold cross-validation is beneficial for model selection, hyperparameter tuning, and determining how well a model would likely perform on untested data. K is frequently set to 5 or 10, however the value can be changed depending on the size and complexity of the dataset.
20th Sept 2023
The Crab Molt Model, a potent linear modeling technique designed for circumstances where two variables exhibit non-normal distribution, skewness, high variance, and high kurtosis, was the focus of our most recent lesson. Predicting pre-molt size from post-molt size is the main goal of this approach. Using information from “Stat Labs: Mathematical Statistics Through Applications, we also investigated the idea of statistical significance, focusing in particular on disparities in means. When building a model and creating a linear plot for post-molt and pre-molt sizes, we discovered a significant variation in means, with the size and shape of these graphs, which are eerily identical, only varied by 14.68 units. The complexity of our project’s three variables prevented the common t-test, which is used for comparisons of two variables, from being used.
18th Sept 2023
A linear regression model with more than one predictor variable, often referred to as multiple linear regression, is a statistical technique used in data analysis and modeling. In this approach, the goal is to establish a linear relationship between a dependent variable and multiple independent predictor variables. Unlike simple linear regression, which involves only one predictor, multiple linear regression allows us to consider the combined impact of several factors on the dependent variable. The model estimates the coefficients for each predictor variable, representing their respective contributions to the variation in the dependent variable. By incorporating multiple predictors, this model enables a more comprehensive understanding of how various factors collectively influence the outcome, making it a valuable tool in fields such as economics, social sciences, and machine learning, where complex relationships between variables need to be explored and quantified.
15th Sept 2023
Today, I went through the linear regression topics i.e Simple Linear Regression and Multiple linear regression.
Simple linear regression is a statistical technique used to model the relationship between a dependent variable and a single independent variable. It provides a straightforward way to understand and quantify the linear association between two variables, with an equation in the form of Y = β0 + β1X + ε, where Y is the dependent variable, X is the independent variable, β0 is the intercept, β1 is the slope, and ε represents the error term.
On the other hand, multiple linear regression extends this concept to accommodate multiple independent variables, allowing for a more complex understanding of how several factors collectively influence the dependent variable. The equation for multiple linear regression is Y = β0 + β1X1 + β2X2 + … + βnXn + ε, where Y is the dependent variable, X1, X2, …, Xn are the independent variables, β0 is the intercept, β1, β2, …, βn are the coefficients for each independent variable, and ε represents the error term. Multiple linear regression is a powerful tool for analyzing complex relationships and making predictions based on multiple factors.
13th Sept 2023
Today’s class provided a comprehensive understanding of the Null Hypothesis and p-value in hypothesis testing. The null hypothesis serves as a foundational assumption in problem-solving, and when we employ proof by contradiction, we aim to either accept it or reject it based on evidence.
The p-value, often referred to as the probability value, plays a crucial role in this process. It quantifies the likelihood of observing results as extreme as what we’ve seen if the null hypothesis were true. When the p-value is exceptionally low, it indicates that the chances of the null hypothesis being correct are minimal, compelling us to reject it in favor of the alternative hypothesis.
In the context of hypothesis testing, sample datasets are analyzed, and the P-value method assists in determining the significance of the null hypothesis. The decision to accept or reject the null hypothesis is influenced by a pre-defined significance level. In general, a lower p-value signifies stronger evidence supporting the rejection of the null hypothesis. Understanding these concepts is pivotal for making informed decisions in statistical analysis.
11th Sept 2023
In today’s class on Simple Linear Regression, several key concepts were covered to better understand the analysis of regression models. Firstly, the discussion delved into skewness, which assesses the asymmetry in the distribution of residuals. Identifying skewness is crucial for assessing the reliability of a regression model and making necessary adjustments. Secondly, kurtosis was highlighted as a metric to assess the distribution of residuals and detect whether they deviate from a normal distribution. Severe kurtosis can impact the validity of regression results. Lastly, heteroscedasticity was discussed, emphasizing how it relates to the varying spread of residuals as independent variables change. Heteroscedasticity can lead to incorrect assessments of statistical significance, affecting parameter estimations and statistical power. The class also introduced the fundamentals of linear regression, a simple supervised learning approach used to predict a continuous dependent variable based on one or more independent variables.
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