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Linear Regression – Assumption – 2 (Inflection Factor.)
Variance Inflection Factor Table Of Contents: What Is VIF? How VIF Works? Mathematical Formula. Interpreting VIF Value. Example Of VIF. Why VIF Is Important? How To Handle High VIF? Summary. (1) What Is VIF? The Variance Inflation Factor (VIF) is a statistical measure used to detect multicollinearity in a regression model. It quantifies how much the variance of a regression coefficient is inflated due to multicollinearity among the independent variables. In simpler terms, VIF helps identify whether a predictor is strongly correlated with other predictors in the model. (2) How VIF Works? If an independent variable is highly correlated with
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Linear Regression – Assumption – 2 (Effect Of Multicollinearity In Regression Model.)
Effect Of Multicollinearity In Regression Model. Table Of Contents: What Is Multicollinearity? Effects Of Multicollinearity. (1) What Is Multicollinearity? Multicollinearity refers to a situation in multiple regression where two or more independent variables are highly correlated. This means that these variables share a significant amount of the same information, making it difficult for the regression model to separate their individual effects on the dependent variable. Here’s how multicollinearity affects regression coefficients: (2) Effects Of Multicollinearity. 1. Instability of Coefficients When multicollinearity exists, small changes in the data can lead to large changes in the estimated regression coefficients. This happens because
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Linear Regression – Assumption – 2 (What Is A Singular Matrix?)
What Is A Singular Matrix? Table Of Contents: What Is A Singular Matrix? (1) What Is A Singular Matrix? A singular matrix is a square matrix that does not have an inverse. This happens when its determinant is equal to zero. In other words, a matrix is singular if it is not full rank, meaning some of its rows or columns are linearly dependent, and they can be expressed as a linear combination of the others. (2) Properties Of A Singular Matrix. (3) Example Of A Singular Matrix. Example-1: Example-2:
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Linear Regression – Assumption – 2 (What Is Standard Error ?)
What Is Standard Error? Table Of Contents: What Is Standard Error? Why Standard Error Is Called Standard ? Factors Affecting Standard Error. Theoretical Range Of Standard Error. Key Concepts In Standard Error. Types Of Standard Error. Mathematical Example Of Standard Error. Why Standard Error Matters? Practical Example Of Standard Error. Linear Regression Coefficients Standard Error. (1) What Is Standard Error? The Standard Error (SE) is a measure of the variability or uncertainty of a statistic, such as a mean, proportion, or regression coefficient, when calculated from a sample. It quantifies how much a sample statistic (e.g., sample mean, xˉbar{x}xˉ) is
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Linear Regression – Evaluation Matrices
Linear Regression – Evaluation Metrices Table Of Contents: Mean Absolute Error. Mean Squared Error. Root Mean Squared Error. R – Squared Error Adjusted R – Squared Error. (1) Mean Absolute Error. Mean Absolute Error calculates the average difference between the calculated values and actual values. It is also known as scale-dependent accuracy as it calculates error in observations taken on the same scale. MAE provides a straightforward measure of the model’s accuracy, as it represents the average magnitude of errors without considering their direction. Formula: Example: To calculate the MAE, we follow these steps: Calculate the absolute differences between the
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Linear Regression – Problem Statements
Linear Regression – Problem Statements (1) Marketing Promotion TV vs Radio vs Social Media Each row corresponds to an independent marketing promotion where the business uses TV, social media, radio, and influencer promotions to increase sales. The features in the data are: TV promotional budget (in “Low,” “Medium,” and “High” categories) Social media promotional budget (in millions of dollars) Radio promotional budget (in millions of dollars) Sales (in millions of dollars) Influencer size (in “Mega,” “Macro,” “Micro,” and “Nano” categories) (2) USA Optimal Product Price Prediction Dataset This dataset contains product prices from Amazon USA, with a focus on price
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Linear Regression : OLS Technique
Linear Regression – OLS Technique. (1) Introduction. The Linear Regression model’s main objective is to find the best-fit line that will closely pass through all the points to minimize the loss. The question here is how to find out the best-fit line. We need some mathematical proof that this is my best-fit line. To solve this problem we have two techniques. Ordinary Least Square Technique. Gradient Descent Technique. (2) Ordinary Least Square Technique. In case of OLS technique we directly use the formula for ‘m’ and ‘b’ to derive the best fit line equation. Here in this vlog we will
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Linear Regression – What Is a Biased Estimator In Linear Regression?
What Is a Biased Estimator In Linear Regression? In linear regression, estimator biasness refers to the systematic deviation of the estimated coefficients from their true population values. A biased estimator consistently produces estimates that, on average, differ from the true values in a predictable manner. In the context of linear regression, the biases of an estimator can occur for different reasons: Omitted Variable Bias: If relevant variables are excluded from the regression model, the estimated coefficients may be biased. Omitted variable bias arises when the omitted variables are correlated with both the independent variables included in the model and the
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Linear Regression – Assumption – 6 (What Is Endogeneity?)
What Is Endogeneity Table Of Contents: What Is Endogeneity? Why Does Endogeneity occur? How To Avoid Endogeneity? (1) What Is Endogeneity? Endogeneity refers to a situation in which there is a correlation or relationship between an explanatory variable and the error term in a statistical model. This correlation can arise when the explanatory variable is influenced by factors that are not accounted for in the model, leading to biased and inconsistent estimates of the model parameters. (2) Why Does Endogeneity Occur ? In the context of regression analysis, endogeneity can occur when one or more of the following conditions are
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Linear Regression – Assumption – 3(Normal Distribution Of Error Term)
Normal Distribution Of Error Term Table Of Contents: What Is A Normal Distribution? Why Normal Distribution Is Matter? Why Is Error Term Should Be Normally Distributed? Remedies For Non-Normal Error Distribution. (1) What Is A Normal Distribution? In a normal distribution, data is symmetrically distributed with no skew. When plotted on a graph, the data follows a bell shape, with most values clustering around a central region and tapering off as they go further away from the center. Normal distributions are also called Gaussian distributions or bell curves because of their shape. (2) Why Normal Distribution Is Important? All kinds of variables in
