presentation on R language Regression in R

ASD

1. REGRESSION IN R B Y KARTHIKEYA SUNKARI VU22CSEN0300384

2. WHAT IS REGRESSION IN R MEAN??

3. SIMPLE LINEAR REGRESSION Simple linear regression investigates how two variables are related to each other. It involves fitting a straight line to the dataset, aiming to minimize the vertical distances from the data points to the line itself. The mathematical representation is expressed as y= mx+by = mx + by= mx+b , where yyy represents the dependent variable and xxx denotes the independent variable. This approach is applicable in scenarios where one particular factor influences the outcome. Simple linear regression provides a useful framework for making predictions and understanding the nature of relationships, making it a valuable tool in various analytical contexts.

4. MPG vs Engine Size

5. Real-Life Example: Predicting Housing Prices with Simple Linear Regression Data Collection : Gather data on house size, number of bedrooms, location, and age as independent variables. Relationship Analysis : Use simple linear regression to determine how house size affects its price. Price Prediction : Predict house prices based on size, aiding buyers and sellers in pricing strategies. Market Insights : Real estate agents utilize regression to analyze market trends for informed decisions. Policy Guidance : Urban planners apply findings to shape housing policies and development strategies.

6. What is Multiple Linear Regression?? Definition : Multiple linear regression is a statistical technique that models the relationship between one dependent variable and two or more independent variables. Application : It is used in various fields, including finance, healthcare, and marketing, to predict outcomes based on multiple factors. Equation : The model is represented by the equation y=b0+b1x1+b2x2+...+ bnxn +ϵy = b_0 + b_1x_1 + b_2x_2 + ... + b_nx_n + \ epsilony =b0​+b1​x1​+b2​x2​+...+bn​ xn ​+ϵ, where yyy is the dependent variable, x1,x2,...,xnx_1, x_2, ..., x_nx1​,x2​,..., xn ​ are independent variables, b0b_0b0​ is the intercept, and b1,b2,...,bnb_1, b_2, ..., b_nb1​,b2​,...,bn​ are the coefficients. Assumptions : Key assumptions include linearity, independence of errors, homoscedasticity, and normality of residuals. Model Evaluation : The model's effectiveness is evaluated using metrics such as R-squared, adjusted R-squared, and p-values for the coefficients to assess significance.

7. Predicting Car Prices with Multiple Linear Regression

8. Real-Life Example: Predicting Student Performance with Multiple Linear Regression Data Collection : Gather data on student characteristics such as study hours, attendance rate, and prior grades. Multiple Factors : Analyze how study habits, attendance, and previous performance together influence final exam scores. Modeling : Use multiple linear regression to create a model that predicts students' final exam scores based on the collected variables. Insights : The model can help educators identify which factors most significantly affect student performance, guiding intervention strategies. Personalization : Schools can tailor support programs based on predictions, improving overall student outcomes and academic success.

9. Logistic Regression Purpose : Logistic regression is used to model the probability of a binary outcome (e.g., success/failure, yes/no) based on one or more independent variables. Sigmoid Function : It applies the logistic function to transform linear combinations of predictors into probabilities, ensuring values fall between 0 and 1. Equation : The model is expressed as p=11+e−(b0+b1x1+b2x2+...+ bnxn )p = \frac{1}{1 + e^{-(b_0 + b_1x_1 + b_2x_2 + ... + b_nx_n )}}p=1+e−(b0​+b1​x1​+b2​x2​+...+bn​ xn ​)1​, where ppp is the probability of the outcome. Applications : Commonly used in fields like healthcare (predicting disease presence), marketing (customer churn), and finance (loan default prediction). Model Evaluation : Performance is assessed using metrics such as accuracy, precision, recall, and the area under the ROC curve (AUC).

10. Predicting Disease Diagnosis with Logistic Regression

11. Real-Life Example: Predicting Credit Default with Logistic Regression Data Collection : Gather data on borrowers, including income, loan amount, credit score, and repayment history. Binary Outcome : The target variable is whether a borrower defaults on a loan (0 = No, 1 = Yes). Model Development : Use logistic regression to model the probability of default based on the collected borrower characteristics. Risk Assessment : The model helps lenders assess risk, enabling them to make informed lending decisions. Improved Strategies : Insights from the model can inform strategies to minimize defaults, such as adjusting lending criteria or offering financial counseling to high-risk borrowers.

12. Comparing Regression Types Simple Linear Regression : Analyzes the relationship between one independent variable and one dependent variable, fitting a straight line to the data. It's straightforward and useful for basic predictions. Multiple Linear Regression : Extends simple linear regression by considering multiple independent variables. It captures complex relationships and interactions among predictors, providing a more comprehensive model. Logistic Regression : Used for binary outcomes, it models the probability of an event occurring based on one or more predictors. Unlike linear regression, it uses the logistic function to ensure predictions are between 0 and 1.

13. Conclusion: Using Regressions in R Powerful Analysis : Regression analysis in R effectively models relationships between variables, providing insights across various fields like healthcare, finance, and marketing. Rich Libraries : R offers numerous packages such as lm () for linear regression and glm () for logistic regression, allowing users to select appropriate methods for their analyses. Data Visualization : R's visualization tools, especially ggplot2 , help illustrate regression results, making it easier to communicate findings to stakeholders. Model Evaluation : R provides metrics like R-squared and diagnostic plots to assess model performance and validate assumptions, ensuring reliable results. Wide Applications : Regression analysis in R can address diverse real-world problems, from predicting sales to assessing health outcomes, making it an essential tool for analysts and researchers.