Vinay Banka’s Post

Linear Regression is one of the most important tools in a Data Scientist's toolbox. Here's everything you need to know in 3 minutes. 1. OLS regression aims to find the best-fitting linear equation that describes the relationship between the dependent variable (often denoted as Y) and independent variables (denoted as X1, X2, ..., Xn). 2. OLS does this by minimizing the sum of the squares of the differences between the observed dependent variable values and those predicted by the linear model. These differences are called "residuals." 3. "Best fit" in the context of OLS means that the sum of the squares of the residuals is as small as possible. Mathematically, it's about finding the values of β0, β1, ..., βn that minimize this sum. 4. Slopes (β1, β2, ..., βn): These coefficients represent the change in the dependent variable for a one-unit change in the corresponding independent variable, holding other variables constant. 5. R-squared (R²): This statistic measures the proportion of variance in the dependent variable that is predictable from the independent variables. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data. 6. t-Statistics and p-Values: For each coefficient, the t-statistic and its associated p-value test the null hypothesis that the coefficient is equal to zero (no effect). A small p-value (< 0.05) suggests that you can reject the null hypothesis. 7. Confidence Intervals: These intervals provide a range of plausible values for each coefficient (usually at the 95% confidence level). Understanding and interpreting these outputs is crucial for assessing the quality of the model, understanding the relationships between variables, and making predictions or conclusions based on the model.

Regression Analysis is a statistical technique used to examine the relationship between one dependent variable and one or more independent (explanatory) variables. It helps to understand how the dependent variable changes when one of the independent variables is varied, while holding other independent variables constant. Regression analysis is commonly used for predictive modelling and for determining the strength of relationships between variables. There are several key types of Regression Analysis: Linear Regression Assumes a linear relationship between the dependent variable and one (simple linear regression) or more (multiple linear regression) independent variables   Logistic Regression Used when the dependent variable is categorical, typically binary (0 or 1). Here, the relationship between the variables is modelled using the logistic function (sigmoid curve) Polynomial Regression A form of linear regression where the relationship between the independent and dependent variables is modelled as an nth-degree polynomial - useful when the data exhibits a curvilinear relationship Ridge and Lasso Regression These are variations of linear regression that apply regularisation techniques to prevent overfitting. Ridge adds a penalty proportional to the sum of the squares of the coefficients, while Lasso adds a penalty proportional to the absolute value of the coefficients. Purposes of Regression Analysis: ⚡ Prediction: Forecasting outcomes based on input variables 👭 Relationship Determination: Identifying and quantifying the strength of relationships between variables 📈 Trend Estimation: Estimating trends and patterns within datasets 🧪 Hypothesis Testing: Testing hypotheses about relationships and the significance of different predictors Regression analysis is a fundamental tool in data science, research, and machine learning for deriving insights from data and making data-driven decisions. Among its many useful applications are prediction of market trends, demand, or pricing, risk assessment, and understanding customer behaviour. #data #datascience #datainsights #DAMAUK

Linear Regression is one of the most important tools in a Data Scientist's toolbox. Here's everything you need to know in 3 minutes. 1. OLS regression aims to find the best-fitting linear equation that describes the relationship between the dependent variable (often denoted as Y) and independent variables (denoted as X1, X2, ..., Xn). 2. OLS does this by minimizing the sum of the squares of the differences between the observed dependent variable values and those predicted by the linear model. These differences are called "residuals." 3. "Best fit" in the context of OLS means that the sum of the squares of the residuals is as small as possible. Mathematically, it's about finding the values of β0, β1, ..., βn that minimize this sum. 4. Slopes (β1, β2, ..., βn): These coefficients represent the change in the dependent variable for a one-unit change in the corresponding independent variable, holding other variables constant. 5. R-squared (R²): This statistic measures the proportion of variance in the dependent variable that is predictable from the independent variables. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data. 6. t-Statistics and p-Values: For each coefficient, the t-statistic and its associated p-value test the null hypothesis that the coefficient is equal to zero (no effect). A small p-value (< 0.05) suggests that you can reject the null hypothesis. 7. Confidence Intervals: These intervals provide a range of plausible values for each coefficient (usually at the 95% confidence level).

#LinearRegression Linear Regression is one of the most important tools in a Data Scientist's toolbox. Here's everything you need to know in 3 minutes. 1. OLS regression aims to find the best-fitting linear equation that describes the relationship between the dependent variable (often denoted as Y) and independent variables (denoted as X1, X2, ..., Xn). 2. OLS does this by minimizing the sum of the squares of the differences between the observed dependent variable values and those predicted by the linear model. These differences are called "residuals." 3. "Best fit" in the context of OLS means that the sum of the squares of the residuals is as small as possible. Mathematically, it's about finding the values of β0, β1, ..., βn that minimize this sum. 4. Slopes (β1, β2, ..., βn): These coefficients represent the change in the dependent variable for a one-unit change in the corresponding independent variable, holding other variables constant. 5. R-squared (R²): This statistic measures the proportion of variance in the dependent variable that is predictable from the independent variables. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data. 6. t-Statistics and p-Values: For each coefficient, the t-statistic and its associated p-value test the null hypothesis that the coefficient is equal to zero (no effect). A small p-value (< 0.05) suggests that you can reject the null hypothesis. 7. Confidence Intervals: These intervals provide a range of plausible values for each coefficient (usually at the 95% confidence level).

Keeping it Linear: Tackling Multicollinearity with PLS Regression 📈📈 Hello everyone! I want to share a recent experience I had while developing a machine learning model for a project. I'm sure many of you can relate to the challenge of choosing the right model and improving performance. In this project, I initially performed exploratory data analysis and was pleased to see a linear trend in my data. I decided to go ahead with linear regression, but when I tested the model on my test data, the performance was disappointing. After some investigation, I identified the presence of multicollinearity among my features as the primary issue. Multicollinearity occurs when two or more features in your dataset are highly correlated, meaning they provide similar information. This can cause issues in regression models as it becomes difficult to determine the unique impact of each feature on the target variable. Fortunately, I discovered a method called Partial Least Squares (PLS) Regression, which is specifically designed to handle multicollinearity. PLS Regression is similar to Principal Component Analysis (PCA) in that it creates new composite variables (components) from the original features. However, while PCA aims to maximize the variance explained, PLS focuses on maximizing the covariance with the response variable within the context of linear regression. For example, let's say we have two features, age and cholesterol, which are highly correlated. PLS Regression will combine these features into a new component that captures the shared information and improves the prediction of the target attribute. This process also helps in dimensionality reduction, making our model more efficient and easier to interpret. By applying PLS Regression, I was able to address the multicollinearity issue and improve the performance of my model. It's a great example of how understanding the underlying causes of poor model performance can lead to simpler and more effective solutions. So, the key takeaway is to keep it linear when possible! PLS Regression is a powerful tool to handle multicollinearity and improve the interpretability of your models. Feel free to share your experiences with multicollinearity and any other techniques you've found useful! Thanks for reading!😊

Here's how to make regression models more "useful" 🧩 A point estimate from a regression model isn’t useful in many cases. Consider you have data from several job roles. There's a model that predicts the expected salary based on job title, years of experience, education level, etc. A regression model will provide a scalar salary estimate based on the inputs. But a single value of, say, $80k isn’t quite useful, is it? If people are using your platform to assess their profile... ...then getting an expected range or quantiles to help them better assess the best-case and worst-case scenarios is MUCH MORE USEFUL to them. - 25th percentile → $65k. This means that 25% of employees in similar roles earn $65k or less. - 50th percentile (the median) → $80k. This represents the middle point in the distribution. - 75th percentile → $95k. This means that 25% of employees earn $95k or more. In fact, following this process makes sense since there’s always a distribution along the target variable. However, a point estimate does not fully reflect that by just outputting the mean. Quantile regression solves this. The idea is to estimate the quantiles of the response variable conditioned on the input. Unlike ordinary least squares (OLS), which estimates the mean of the dependent variable for given values of the predictors... ...Quantile regression can provide estimates for various quantiles, such as the 25th, 50th, and 75th percentiles. In my experience, these models typically work pretty well with tree-based regression models. In fact, models like lightgbm regression inherently support quantile objection functions. I published a visual explanation of how it works in the Daily Dose of Data Science newsletter if you want to learn more: https://lnkd.in/d95ZFNmt. 👉 Over to you: There are several ways you can make use of Quantile regression in your models. Can you identify one??

🚀 𝗨𝗻𝗱𝗲𝗿𝘀𝘁𝗮𝗻𝗱𝗶𝗻𝗴 𝗠𝗲𝘁𝗿𝗶𝗰𝘀 𝘁𝗼 𝗠𝗲𝗮𝘀𝘂𝗿𝗲 𝘁𝗵𝗲 𝗚𝗼𝗼𝗱𝗻𝗲𝘀𝘀 𝗼𝗳 𝗙𝗶𝘁 𝗶𝗻 𝗟𝗶𝗻𝗲𝗮𝗿 𝗥𝗲𝗴𝗿𝗲𝘀𝘀𝗶𝗼𝗻 Linear regression is one of the most widely used algorithms in Data Science and Machine Learning. Let’s explore key metrics used to assess a regression model’s performance, along with why and when they’re helpful. 𝟭. 𝗠𝗲𝗮𝗻 𝗦𝗾𝘂𝗮𝗿𝗲𝗱 𝗘𝗿𝗿𝗼𝗿 (𝗠𝗦𝗘) The Mean Squared Error calculates the average squared difference between predicted and actual values. Since the errors are squared, MSE penalizes larger errors more than smaller ones. This makes it particularly sensitive to outliers. 𝟮. 𝗥𝗼𝗼𝘁 𝗠𝗲𝗮𝗻 𝗦𝗾𝘂𝗮𝗿𝗲𝗱 𝗘𝗿𝗿𝗼𝗿 (𝗥𝗠𝗦𝗘) The Root Mean Squared Error is the square root of MSE, bringing the error measure back to the same units as the target variable. By providing error values in the original units, RMSE is easier to interpret in real-world terms. 𝟯. 𝗠𝗲𝗮𝗻 𝗔𝗯𝘀𝗼𝗹𝘂𝘁𝗲 𝗘𝗿𝗿𝗼𝗿 (𝗠𝗔𝗘) The Mean Absolute Error computes the average absolute difference between predicted and actual values. Unlike MSE and RMSE, which disproportionately penalize larger errors, MAE treats all errors equally. This makes it more robust to outliers compared to squared-error metrics. 𝟰. 𝗥𝗲𝘀𝗶𝗱𝘂𝗮𝗹 𝗦𝘁𝗮𝗻𝗱𝗮𝗿𝗱 𝗘𝗿𝗿𝗼𝗿 (𝗥𝗦𝗘) The Residual Standard Error quantifies the average deviation of observed values from the regression line. A smaller RSE value indicates a better fit, as it suggests that the predictions are closer to the observed data. 𝟱. 𝗥𝟮 𝗦𝘁𝗮𝘁𝗶𝘀𝘁𝗶𝗰 The R² statistic, or coefficient of determination, measures the proportion of variance in the target variable that is explained by the model. An R² value closer to 1 indicates that the model explains a large proportion of the variability in the data, while a value near 0 implies the model explains very little. Each metric offers unique insights, so choose based on the problem and context! 💡 #DataScience #MachineLearning #InterviewPreparation #LinearRegression

Logistic regression is a must-know model for data scientists. Here's what you should know in 7 steps ↓ 1️⃣ 𝗢𝘃𝗲𝗿𝘃𝗶𝗲𝘄 It's a go-to model for predicting binary outcomes (e.g. yes/no, spam/ham) 2️⃣ 𝗠𝗮𝘁𝗵 It uses a sigmoid function to fit an S-shaped curve on binary outcomes. This transformation expresses the outcomes in probability form. 3️⃣ 𝗧𝗿𝗮𝗶𝗻𝗶𝗻𝗴 Maximum likelihood estimation is used to fit the model on data. The performance is evaluated using metrics like F1-score and ROC-AUC. 4️⃣ 𝗜𝗻𝘁𝗲𝗿𝗽𝗿𝗲𝘁𝗮𝘁𝗶𝗼𝗻 Interpret predictors in odds-ratio (OR). ↳ OR > 1: One unit increase in X increases the odds of an event ↳ OR < 1: One unit increase in X decreases the odds of an event ↳ OR = 1: Change in X has no effect on the odds of an event Interpret significance and uncertainty using P-value and CI of the predictor. 5️⃣ 𝗔𝘀𝘀𝘂𝗺𝗽𝘁𝗶𝗼𝗻𝘀 → Independent observations → No multicollinearity among predictors → Linear relationship between the logit of the outcome and predictors 6️⃣ 𝗔𝗽𝗽𝗹𝗶𝗰𝗮𝘁𝗶𝗼𝗻𝘀 ↳ Marketing: Predict customer churn ↳ Finance: Predict credit risk ↳ Healthcare: Predict disease 7️⃣ 𝗜𝗻𝘁𝗲𝗿𝘃𝗶𝗲𝘄 𝗤𝘂𝗲𝘀𝘁𝗶𝗼𝗻𝘀 Questions I've encountered in interviews and also from my client's interview experiences: 1. What is the logistic regression model? 2. How do you interpret the logistic regression model? 3. What's the difference between the linear and logistic models? 4. How do you interpret the confidence interval of a logistic regression model? via DataInterview.com #datascientist #datascience #logisticRegression

*** Linear Discriminate Analysis: Explained and Its History *** ~ Linear discriminant analysis(LDA) is a generalization of Fisher's linear discriminant, a method used in statistics and other fields to find a linear combination of features that characterizes or separates two or more classes of objects or events. ~ The resulting combination may be used as a linear classifier or, more commonly, for dimensionality reduction before later classification. ~ LDA is closely related to the analysis of variance (ANOVA) and regression analysis, which also attempt to express one dependent variable as a linear combination of other features or measurements. ~ However, ANOVA uses categorical independent variables and a continuous dependent variable, whereas discriminant analysis has continuous independent variables and a categorical dependent variable (i.e., the class label). ~ Logistic regression and probit regression are more similar to LDA than ANOVA, as they also explain a categorical variable by the values of continuous independent variables. ~ These other methods are preferable in applications where it is not reasonable to assume that the independent variables are normally distributed, which is a fundamental assumption of the LDA method. ~ LDA is also closely related to principal component analysis (PCA) and factor analysis in that they both look for linear combinations of variables that best explain the data. ~ LDA explicitly attempts to model the difference between the classes of data. In contrast, PCA does not consider any difference in class, and factor analysis builds the feature combinations based on differences rather than similarities. ~ Discriminant analysis is also different from factor analysis in that it is not an interdependence technique: a distinction between independent and dependent variables (also called criterion variables) must be made. ~ LDA works when the measurements of independent variables for each observation are continuous quantities. When dealing with categorical independent variables, the equivalent technique is discriminant correspondence analysis. ~ Discriminant analysis is used when groups are known a priori. Each case must have a score on one or more quantitative predictor measures and a score on a group measure. ~ In simple terms, discriminant function analysis is classification - distributing things into groups, classes, or categories of the same type. ~ The original dichotomous discriminant analysis was developed by Sir Ronald Fisher in 1936. ~ It differs from an ANOVA or MANOVA, which is used to predict one (ANOVA) or multiple (MANOVA) continuous dependent variables by one or more independent categorical variables. ~ Discriminant function analysis helps determine whether a set of variables effectively predicts category membership. --- B. Noted