This document provides an overview of simple linear regression analysis. It discusses estimating regression coefficients using the least squares method, interpreting the regression equation, assessing model fit using measures like the standard error of the estimate and coefficient of determination, testing hypotheses about regression coefficients, and using the regression model to make predictions.
In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'Criterion Variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a probability distribution.
In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'Criterion Variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a probability distribution.
Simple Linear Regression: Step-By-StepDan Wellisch
This presentation was made to our meetup group found here.: https://www.meetup.com/Chicago-Technology-For-Value-Based-Healthcare-Meetup/ on 9/26/2017. Our group is focused on technology applied to healthcare in order to create better healthcare.
Simple Regression presentation is a
partial fulfillment to the requirement in PA 297 Research for Public Administrators, presented by Atty. Gayam , Dr. Cabling and Mr. Cagampang
Simple Linear Regression: Step-By-StepDan Wellisch
This presentation was made to our meetup group found here.: https://www.meetup.com/Chicago-Technology-For-Value-Based-Healthcare-Meetup/ on 9/26/2017. Our group is focused on technology applied to healthcare in order to create better healthcare.
Simple Regression presentation is a
partial fulfillment to the requirement in PA 297 Research for Public Administrators, presented by Atty. Gayam , Dr. Cabling and Mr. Cagampang
A quick introduction to linear and logistic regression using Python. Part of the Data Science Bootcamp held in Amman by the Jordan Open Source Association Dec/Jan 2015. Reference code can be found on Github https://github.com/jordanopensource/data-science-bootcamp/tree/master/MachineLearning/Session1
Introduction to linear regression and the maths behind it like line of best fit, regression matrics. Other concepts include cost function, gradient descent, overfitting and underfitting, r squared.
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Chapter 10: Correlation and Regression
10.2: Regression
Applied Numerical Methods Curve Fitting: Least Squares Regression, InterpolationBrian Erandio
Correction with the misspelled langrange.
and credits to the owners of the pictures (Fantasmagoria01, eugene-kukulka, vooga, and etc.) . I do not own all of the pictures used as background sorry to those who aren't tagged.
The presentation contains topics from Applied Numerical Methods with MATHLAB for Engineers and Scientist 6th and International Edition.
linear regression is a linear approach for modelling a predictive relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables), which are measured without error. The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable. If the explanatory variables are measured with error then errors-in-variables models are required, also known as measurement error models.
In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, the conditional mean of the response given the values of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuses on the conditional probability distribution of the response given the values of the predictors, rather than on the joint probability distribution of all of these variables, which is the domain of multivariate analysis.
Linear regression was the first type of regression analysis to be studied rigorously, and to be used extensively in practical applications.[4] This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine.
Linear regression has many practical uses. Most applications fall into one of the following two broad categories:
If the goal is error reduction in prediction or forecasting, linear regression can be used to fit a predictive model to an observed data set of values of the response and explanatory variables. After developing such a model, if additional values of the explanatory variables are collected without an accompanying response value, the fitted model can be used to make a prediction of the response.
If the goal is to explain variation in the response variable that can be attributed to variation in the explanatory variables, linear regression analysis can be applied to quantify the strength of the relationship between the response and the explanatory variables, and in particular to determine whether some explanatory variables may have no linear relationship with the response at all, or to identify which subsets of explanatory variables may contain redundant information about the response.
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Chapter 10: Correlation and Regression
10.1: Correlation
Discover the innovative and creative projects that highlight my journey throu...dylandmeas
Discover the innovative and creative projects that highlight my journey through Full Sail University. Below, you’ll find a collection of my work showcasing my skills and expertise in digital marketing, event planning, and media production.
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Cultivating and maintaining discipline within teams is a critical differentiator for successful organisations.
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Improving profitability for small businessBen Wann
In this comprehensive presentation, we will explore strategies and practical tips for enhancing profitability in small businesses. Tailored to meet the unique challenges faced by small enterprises, this session covers various aspects that directly impact the bottom line. Attendees will learn how to optimize operational efficiency, manage expenses, and increase revenue through innovative marketing and customer engagement techniques.
Business Valuation Principles for EntrepreneursBen Wann
This insightful presentation is designed to equip entrepreneurs with the essential knowledge and tools needed to accurately value their businesses. Understanding business valuation is crucial for making informed decisions, whether you're seeking investment, planning to sell, or simply want to gauge your company's worth.
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Enterprise excellence and inclusive excellence are closely linked, and real-world challenges have shown that both are essential to the success of any organization. To achieve enterprise excellence, organizations must focus on improving their operations and processes while creating an inclusive environment that engages everyone. In this interactive session, the facilitator will highlight commonly established business practices and how they limit our ability to engage everyone every day. More importantly, though, participants will likely gain increased awareness of what we can do differently to maximize enterprise excellence through deliberate inclusion.
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Marvin neemt je in deze presentatie mee in de voordelen van non-endemic advertising op retail media netwerken. Hij brengt ook de uitdagingen in beeld die de markt op dit moment heeft op het gebied van retail media voor niet-leveranciers.
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Sustainability has become an increasingly critical topic as the world recognizes the need to protect our planet and its resources for future generations. Sustainability means meeting our current needs without compromising the ability of future generations to meet theirs. It involves long-term planning and consideration of the consequences of our actions. The goal is to create strategies that ensure the long-term viability of People, Planet, and Profit.
Leading companies such as Nike, Toyota, and Siemens are prioritizing sustainable innovation in their business models, setting an example for others to follow. In this Sustainability training presentation, you will learn key concepts, principles, and practices of sustainability applicable across industries. This training aims to create awareness and educate employees, senior executives, consultants, and other key stakeholders, including investors, policymakers, and supply chain partners, on the importance and implementation of sustainability.
LEARNING OBJECTIVES
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CONTENTS
1. Introduction and Key Concepts of Sustainability
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3. Measures and Reporting in Sustainability
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To download the complete presentation, visit: https://www.oeconsulting.com.sg/training-presentations
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As an Army veteran dedicated to lifelong learning, I bring a disciplined, strategic mindset to my pursuits. I am constantly expanding my knowledge to innovate and lead effectively. My journey is driven by a commitment to excellence, and to make a meaningful impact in the world.
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What is the TDS Return Filing Due Date for FY 2024-25.pdfseoforlegalpillers
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Unveiling the Secrets How Does Generative AI Work.pdfSam H
At its core, generative artificial intelligence relies on the concept of generative models, which serve as engines that churn out entirely new data resembling their training data. It is like a sculptor who has studied so many forms found in nature and then uses this knowledge to create sculptures from his imagination that have never been seen before anywhere else. If taken to cyberspace, gans work almost the same way.
Unveiling the Secrets How Does Generative AI Work.pdf
Simple lin regress_inference
1. Simple Linear Regression 1. review of least squares procedure 2. inference for least squares lines
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3. The Model House size House Cost Most lots sell for $25,000 Building a house costs about $75 per square foot. House cost = 25000 + 75(Size) The model has a deterministic and a probabilistic components
4. The Model House cost = 25000 + 75(Size) House size House Cost Most lots sell for $25,000 However, house cost vary even among same size houses! Since cost behave unpredictably, we add a random component.
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7. The Least Squares (Regression) Line A good line is one that minimizes the sum of squared differences between the points and the line.
8. The Least Squares (Regression) Line 3 3 4 4 (1,2) 2 2 (2,4) (3,1.5) Sum of squared differences = (2 - 1) 2 + (4 - 2) 2 + (1.5 - 3) 2 + (4,3.2) (3.2 - 4) 2 = 6.89 2.5 Let us compare two lines The second line is horizontal The smaller the sum of squared differences the better the fit of the line to the data. 1 1 Sum of squared differences = (2 -2.5) 2 + (4 - 2.5) 2 + (1.5 - 2.5) 2 + (3.2 - 2.5) 2 = 3.99
9. The Estimated Coefficients To calculate the estimates of the slope and intercept of the least squares line , use the formulas: The regression equation that estimates the equation of the first order linear model is: Alternate formula for the slope b 1
14. Interpreting the Linear Regression -Equation This is the slope of the line. For each additional mile on the odometer, the price decreases by an average of $0.0623 The intercept is b 0 = $17067. 0 No data Do not interpret the intercept as the “ Price of cars that have not been driven” 17067
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16. The Normality of From the first three assumptions we have: y is normally distributed with mean E(y) = 0 + 1 x, and a constant standard deviation x 1 x 2 x 3 The standard deviation remains constant, but the mean value changes with x 0 + 1 x 1 0 + 1 x 2 0 + 1 x 3 E(y|x 2 ) E(y|x 3 ) E(y|x 1 )
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28. Coefficient of determination x 1 x 2 y 1 y 2 Two data points (x 1 ,y 1 ) and (x 2 ,y 2 ) of a certain sample are shown. Total variation in y = Variation explained by the regression line + Unexplained variation (error) Variation in y = SSR + SSE y
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43. For each residual we calculate the standard deviation as follows: A Partial list of Standard residuals Residual Analysis Standardized residual ‘i’ = Residual ‘i’ Standard deviation
44. It seems the residual are normally distributed with mean zero Residual Analysis
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48. Patterns in the appearance of the residuals over time indicates that autocorrelation exists. + + + + + + + + + + + + + + + + + + + + + + + + + Time Residual Residual Time + + + Note the runs of positive residuals, replaced by runs of negative residuals Note the oscillating behavior of the residuals around zero. 0 0 Non Independence of Error Variables
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50. + + + + + + + + + + + + + + + + The outlier causes a shift in the regression line … but, some outliers may be very influential An outlier An influential observation + + + + + + + + + + +
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