The document summarizes key concepts from Chapter 13 of McGraw-Hill's Linear Regression and Correlation textbook. It discusses regression analysis and its uses in exploring relationships between variables. It introduces important terms like dependent and independent variables. It also covers calculating and interpreting the coefficient of correlation and coefficient of determination to measure the strength of relationships between variables. Additionally, it discusses developing linear regression models and least squares regression lines to estimate dependent variables based on independent variables. It provides examples of applying these concepts to real data sets.
The document discusses correlation and linear regression analysis. It defines key terms like dependent and independent variables and introduces the correlation coefficient r, which measures the strength and direction of the linear relationship between two variables. The value of r can range from -1 to 1, with values closer to these extremes indicating a stronger correlation. Regression analysis uses the independent variable to estimate the dependent variable based on a linear regression equation determined by the least squares method. Examples are provided to demonstrate how to calculate r, generate a regression equation, and use the equation to interpret the linear relationship between two variables through measures like the standard error of estimate and confidence and prediction intervals.
The process of describing populations and samples is called Descriptive Statistics. A population includes everyone in the area of interest. For example, every person in the United States, every dog owner in Florida, or every computer user in the world. A sample is a small piece of the whole (i.e. 1000 people in the United States, 250 Floridian dog owners, 2500 worldwide computer users). There are three main ways to describe populations and samples: central tendency, dispersion and association.
1. The document outlines the process of estimating demand functions using statistical techniques, including identifying variables, collecting data, specifying models, and estimating parameters.
2. Linear and nonlinear models are discussed for relating dependent and independent variables, with the linear model being most common. Estimating techniques include ordinary least squares regression.
3. Regression results can be used to interpret relationships between variables and make predictions, though correlation does not necessarily imply causation. Testing procedures evaluate the model fit and significance of relationships.
Multiple Linear Regression is a statistical technique that is designed to explore the relationship between two or more. It is useful in identifying important factors that will affect a dependent variable, and the nature of the relationship between each of the factors and the dependent variable. It can help an enterprise consider the impact of multiple independent predictors and variables on a dependent variable, and is beneficial for forecasting and predicting results.
CRAM (Change Risk Assessment Model) is a novel model approach which can significantly contribute to the missing formality of business models especially in the change(s) risk assessment area.
Project Management has long established the need for risk management techniques to be utilised in the succinct definition of associated risks in projects and agreement on countervailing actions as an aim to reduce scope creep, increase the probability of on-time and in-budget delivery.
Uncontrolled changes, regardless of size and complexity, can certainly pose as risks, of any magnitude, to projects and affect project success or even an organisation’s coherence.
Generalized Linear Regression with Gaussian Distribution is a statistical technique which is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution. The Generalized Linear Model (GLM) generalizes linear regression by allowing the linear model to be related to the response variable via a link function (in this case link function being Gaussian Distribution) and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.
The document discusses simple linear regression and multiple linear regression. It provides an example of using simple linear regression to model the relationship between sales (SALESt) and advertising (ADVERTt) using yearly data from 1907 to 1960. A scatter plot shows an apparent linear relationship between the variables. Estimation of the regression model finds the line of best fit to be SALESt = 488.8 + 1.4 ADVERTt. Diagnostic checks examine how well the model fits the data and whether advertising is a significant predictor of sales. A second model is discussed using lagged sales (SALESt-1) as the predictor, which is found to fit the data even better.
The document discusses correlation and linear regression analysis. It defines key terms like dependent and independent variables and introduces the correlation coefficient r, which measures the strength and direction of the linear relationship between two variables. The value of r can range from -1 to 1, with values closer to these extremes indicating a stronger correlation. Regression analysis uses the independent variable to estimate the dependent variable based on a linear regression equation determined by the least squares method. Examples are provided to demonstrate how to calculate r, generate a regression equation, and use the equation to interpret the linear relationship between two variables through measures like the standard error of estimate and confidence and prediction intervals.
The process of describing populations and samples is called Descriptive Statistics. A population includes everyone in the area of interest. For example, every person in the United States, every dog owner in Florida, or every computer user in the world. A sample is a small piece of the whole (i.e. 1000 people in the United States, 250 Floridian dog owners, 2500 worldwide computer users). There are three main ways to describe populations and samples: central tendency, dispersion and association.
1. The document outlines the process of estimating demand functions using statistical techniques, including identifying variables, collecting data, specifying models, and estimating parameters.
2. Linear and nonlinear models are discussed for relating dependent and independent variables, with the linear model being most common. Estimating techniques include ordinary least squares regression.
3. Regression results can be used to interpret relationships between variables and make predictions, though correlation does not necessarily imply causation. Testing procedures evaluate the model fit and significance of relationships.
Multiple Linear Regression is a statistical technique that is designed to explore the relationship between two or more. It is useful in identifying important factors that will affect a dependent variable, and the nature of the relationship between each of the factors and the dependent variable. It can help an enterprise consider the impact of multiple independent predictors and variables on a dependent variable, and is beneficial for forecasting and predicting results.
CRAM (Change Risk Assessment Model) is a novel model approach which can significantly contribute to the missing formality of business models especially in the change(s) risk assessment area.
Project Management has long established the need for risk management techniques to be utilised in the succinct definition of associated risks in projects and agreement on countervailing actions as an aim to reduce scope creep, increase the probability of on-time and in-budget delivery.
Uncontrolled changes, regardless of size and complexity, can certainly pose as risks, of any magnitude, to projects and affect project success or even an organisation’s coherence.
Generalized Linear Regression with Gaussian Distribution is a statistical technique which is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution. The Generalized Linear Model (GLM) generalizes linear regression by allowing the linear model to be related to the response variable via a link function (in this case link function being Gaussian Distribution) and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.
The document discusses simple linear regression and multiple linear regression. It provides an example of using simple linear regression to model the relationship between sales (SALESt) and advertising (ADVERTt) using yearly data from 1907 to 1960. A scatter plot shows an apparent linear relationship between the variables. Estimation of the regression model finds the line of best fit to be SALESt = 488.8 + 1.4 ADVERTt. Diagnostic checks examine how well the model fits the data and whether advertising is a significant predictor of sales. A second model is discussed using lagged sales (SALESt-1) as the predictor, which is found to fit the data even better.
This chapter discusses various methods for describing and exploring data, including dot plots, percentiles, box plots, and scatter diagrams. Dot plots display each data point along a number line and are useful for small data sets. Percentiles divide a data set into equal percentages and are used to calculate quartiles. Box plots graphically depict the center, spread, and outliers of a data set. Scatter diagrams show the relationship between two variables by plotting one on the x-axis and one on the y-axis. Contingency tables organize counts of observations into categories to study relationships between nominal or ordinal variables.
This document discusses correlation and linear regression analysis. It begins by explaining the purpose of correlation analysis is to analyze relationships between two quantitative variables and measure the strength and direction of that relationship using the correlation coefficient r. It then discusses how to calculate r to test relationships between variables. The document proceeds to explain linear regression analysis estimates the linear relationship between two variables with an equation in the form of Y = a + bX. It provides examples of applying regression analysis and interpreting the slope, intercept, and coefficient of determination.
Multiple Linear Regression is a statistical technique that is designed to explore the relationship between two or more. It is useful in identifying important factors that will affect a dependent variable, and the nature of the relationship between each of the factors and the dependent variable. It can help an enterprise consider the impact of multiple independent predictors and variables on a dependent variable, and is beneficial for forecasting and predicting results.
This document discusses multiple regression analysis. It begins by introducing multiple regression as an extension of simple linear regression that allows for modeling relationships between a response variable and multiple explanatory variables. It then covers topics such as examining variable distributions, building regression models, estimating model parameters, and assessing overall model fit and significance of individual predictors. An example demonstrates using multiple regression to build a model for predicting cable television subscribers based on advertising rates, station power, number of local families, and number of competing stations.
8
The document provides an overview of marketing engineering and response models. It discusses linear regression models, which assume a linear relationship between dependent and independent variables. Key points include:
1) Linear regression finds coefficients that minimize error between actual and predicted dependent variable values.
2) Diagnostics include R-squared, standard error, and ANOVA tables comparing explained, residual, and total variation.
3) Models can forecast sales and profits given marketing mix changes.
4) Logit models are used when dependent variables are binary or limited ranges, predicting choice probabilities rather than continuous preferences.
This chapter discusses various methods for summarizing and exploring data, including dot plots, stem-and-leaf displays, percentiles, box plots, and scatter plots. Dot plots and stem-and-leaf displays organize data in a way that shows the distribution while maintaining each data point. Percentiles such as the median and quartiles divide data into equal portions. Box plots graphically show the center, spread, and outliers of data. Scatter plots reveal relationships between two variables, while contingency tables summarize categorical data relationships.
Isotonic Regression is a statistical technique of fitting a free-form line to a sequence of observations such that the fitted line is non-decreasing (or non-increasing) everywhere, and lies as close to the observations as possible. Isotonic Regression is limited to predicting numeric output so the dependent variable must be numeric in nature…
This document discusses quantitative research methods including correlation, simple linear regression, and multiple regression. It provides examples of how to conduct simple linear regression using SPSS to analyze the relationship between two variables and predict the dependent variable based on the independent variable. It then expands the discussion to multiple linear regression, using SPSS to analyze the relationships between multiple independent variables and one dependent variable. Key steps of assessing the model such as the coefficient of determination and F-test of ANOVA are also covered.
This document discusses performance metrics for evaluating machine learning models. It explains that metrics are used to understand how well a model performs on both the training data and new, unseen data. For classification models, common metrics include accuracy, confusion matrix, precision, recall, F1 score, and AUC. For regression models, common metrics are mean absolute error, mean squared error, R2 score, and adjusted R2. The document provides formulas and explanations for calculating and interpreting each of these important performance metrics.
This document discusses performance metrics for evaluating machine learning models. It explains that performance metrics help understand how well a model performs on its training data and new, unseen data. For classification models, common metrics include accuracy, confusion matrix, precision, recall, F1 score, and AUC. For regression models, common metrics are mean absolute error, mean squared error, R2 score, and adjusted R2. The document provides formulas and explanations for calculating and interpreting each of these important performance metrics.
The document discusses the chi-square test of independence and provides examples of applying it. It first defines the chi-square test and explains that it determines if there is a significant relationship between two categorical variables. Then, it analyzes four problems using a chi-square test to assess relationships between variables like product purchased and customer gender, region and computer ownership, current and preferred smartphone brand, and alcohol drinking and smoking habits. The document demonstrates how to set up and interpret the results of chi-square tests, including observing frequencies, calculating test statistics, and determining if relationships are statistically significant.
Journal ArticleSales and Dealership Size as a Pred.docxcroysierkathey
Journal Article
Sales and Dealership Size as a Predictor of a Store’s Profit
Abstract
This study aims to know if a dealership’s size and sales could affect the owner’s profit. The statistical analysis that was used is multiple linear regression analysis. The results showed that a dealership’s size can explain 94.46% of the owner’s profit. On the other hand, the sales in both Sedans and SUV’s can explain 79.26% of the owner’s profit. Other than that, the analysis also showed that the increase in dealership size by a thousand sq. ft can also increase the profit by 11 940. For the sales, an increase in Sedan sales by one could increase the profit by 2 320 and an increase in SUV sales by one could increase the profit by 4 790. All of the coefficients and the regression models are proven significant and reliable by using multiple hypothesis testing. By using these results, a person aspiring to be a retailer owner would know what to increase so that his/her profits would increase too.
SALES AND DEALERSHIP SIZE AS A PREDICTOR OF A STORE’S PROFIT
Establishing a store is easy because all that is needed is an initial investment and good management skills. The challenging task to do is making that store successful. There are many factors that could affect a store’s monthly profit. The mere design of a retailer, including color and interior design, can increase the owner’s profit. One measurable factor that could affect revenue is the owner’s initial investment. If the owner is willing to risk a lot, then the possible income would be more than that. In the end, knowing how much one factor can affect a store’s profit is a desirable trait. It can be achieved easily by using regression analysis in Microsoft Excel or SPSS. Getting the data is easy but interpreting the data can be difficult.
METHODOLOGY
Linear regression and multiple linear regression analysis are both thorough methods of determining correlation and determination. This is the statistical analysis used. By using Microsoft Excel’s Analyst Tool Pack, summary outputs of regression statistics and ANOVA was able to be gathered. The summary outputs are attached in the appendices. From those analyses, the equations for the predicted value of profit based on the independent variables were created. Other than the equations, their characteristics are also present, such as the standard error, t-stat, p-value, and F value. Standard error of a statistic is the standard deviation of the data, which uses sampling distribution (Everett). In regression, it is the standard error of the regression coefficient. P-value is the probability value for a given statistical data is the same or greater than the number of the observed (Wasserstein and Lazar). F value is used to compare the data that has been fitted to another data set to check if the sample can represent the population (Lomax). Lastly, the t-statistic is the proportion of how far the value of a restriction is from a computed value to its stan ...
The document discusses linear regression analysis. It defines a regression equation as an equation that expresses the linear relationship between two variables. It explains that regression analysis uses the independent variable (X) to estimate the dependent variable (Y), and that the relationship is determined using the least squares method to minimize the difference between predicted and actual Y values. It provides an example of finding the regression equation relating number of sales calls to copiers sold.
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.
Linear regression is a statistical method used to explain the relationship between variables. The document discusses:
1) An agenda covering regression, diagnostics, differences between linear and logistic regression, assumptions, and interview questions.
2) Details on linear regression including understanding the algorithm, assumptions around linearity, normality, multicollinearity, autocorrelation, and homoscedasticity.
3) How to check if assumptions are violated including residual plots, Q-Q plots, and various statistical tests.
The document provides an in-depth overview of linear regression modeling, assumptions, and how to diagnose potential issues.
This chapter discusses various methods for describing and exploring quantitative data, including dot plots, stem-and-leaf displays, percentiles, box plots, measures of skewness, scatter diagrams, and contingency tables. It provides examples and explanations of how to construct and interpret each method. Key goals are to develop an understanding of distributions and relationships within data sets.
This document provides an overview of regression analysis, including:
- Regression analysis is used to study the relationship between variables and predict one variable from another. It can be linear or non-linear.
- Simple regression involves one independent and one dependent variable, while multiple regression involves two or more independent variables.
- The method of least squares is used to determine the regression equation that best fits the data by minimizing the sum of the squared residuals.
This overview discusses the predictive analytical technique known as Gradient Boosting Regression, an analytical technique that explore the relationship between two or more variables (X, and Y). Its analytical output identifies important factors ( Xi ) impacting the dependent variable (y) and the nature of the relationship between each of these factors and the dependent variable. Gradient Boosting Regression is limited to predicting numeric output so the dependent variable has to be numeric in nature. The minimum sample size is 20 cases per independent variable. The Gradient Boosting Regression technique is useful in many applications, e.g., targeted sales strategies by using appropriate predictors to ensure accuracy of marketing campaigns and clarify relationships among factors such as seasonality, product pricing and product promotions, or for an agriculture business attempting to ascertain the effects of temperature, rainfall and humidity on crop production. Gradient Boosting Regression is just one of the numerous predictive analytical techniques and algorithms included in the Assisted Predictive Modeling module of the Smarten augmented analytics solution. This solution is designed to serve business users with sophisticated tools that are easy to use and require no data science or technical skills. Smarten is a representative vendor in multiple Gartner reports including the Gartner Modern BI and Analytics Platform report and the Gartner Magic Quadrant for Business Intelligence and Analytics Platforms Report.
STATATHON: Unleashing the Power of Statistics in a 48-Hour Knowledge Extravag...sameer shah
"Join us for STATATHON, a dynamic 2-day event dedicated to exploring statistical knowledge and its real-world applications. From theory to practice, participants engage in intensive learning sessions, workshops, and challenges, fostering a deeper understanding of statistical methodologies and their significance in various fields."
This chapter discusses various methods for describing and exploring data, including dot plots, percentiles, box plots, and scatter diagrams. Dot plots display each data point along a number line and are useful for small data sets. Percentiles divide a data set into equal percentages and are used to calculate quartiles. Box plots graphically depict the center, spread, and outliers of a data set. Scatter diagrams show the relationship between two variables by plotting one on the x-axis and one on the y-axis. Contingency tables organize counts of observations into categories to study relationships between nominal or ordinal variables.
This document discusses correlation and linear regression analysis. It begins by explaining the purpose of correlation analysis is to analyze relationships between two quantitative variables and measure the strength and direction of that relationship using the correlation coefficient r. It then discusses how to calculate r to test relationships between variables. The document proceeds to explain linear regression analysis estimates the linear relationship between two variables with an equation in the form of Y = a + bX. It provides examples of applying regression analysis and interpreting the slope, intercept, and coefficient of determination.
Multiple Linear Regression is a statistical technique that is designed to explore the relationship between two or more. It is useful in identifying important factors that will affect a dependent variable, and the nature of the relationship between each of the factors and the dependent variable. It can help an enterprise consider the impact of multiple independent predictors and variables on a dependent variable, and is beneficial for forecasting and predicting results.
This document discusses multiple regression analysis. It begins by introducing multiple regression as an extension of simple linear regression that allows for modeling relationships between a response variable and multiple explanatory variables. It then covers topics such as examining variable distributions, building regression models, estimating model parameters, and assessing overall model fit and significance of individual predictors. An example demonstrates using multiple regression to build a model for predicting cable television subscribers based on advertising rates, station power, number of local families, and number of competing stations.
8
The document provides an overview of marketing engineering and response models. It discusses linear regression models, which assume a linear relationship between dependent and independent variables. Key points include:
1) Linear regression finds coefficients that minimize error between actual and predicted dependent variable values.
2) Diagnostics include R-squared, standard error, and ANOVA tables comparing explained, residual, and total variation.
3) Models can forecast sales and profits given marketing mix changes.
4) Logit models are used when dependent variables are binary or limited ranges, predicting choice probabilities rather than continuous preferences.
This chapter discusses various methods for summarizing and exploring data, including dot plots, stem-and-leaf displays, percentiles, box plots, and scatter plots. Dot plots and stem-and-leaf displays organize data in a way that shows the distribution while maintaining each data point. Percentiles such as the median and quartiles divide data into equal portions. Box plots graphically show the center, spread, and outliers of data. Scatter plots reveal relationships between two variables, while contingency tables summarize categorical data relationships.
Isotonic Regression is a statistical technique of fitting a free-form line to a sequence of observations such that the fitted line is non-decreasing (or non-increasing) everywhere, and lies as close to the observations as possible. Isotonic Regression is limited to predicting numeric output so the dependent variable must be numeric in nature…
This document discusses quantitative research methods including correlation, simple linear regression, and multiple regression. It provides examples of how to conduct simple linear regression using SPSS to analyze the relationship between two variables and predict the dependent variable based on the independent variable. It then expands the discussion to multiple linear regression, using SPSS to analyze the relationships between multiple independent variables and one dependent variable. Key steps of assessing the model such as the coefficient of determination and F-test of ANOVA are also covered.
This document discusses performance metrics for evaluating machine learning models. It explains that metrics are used to understand how well a model performs on both the training data and new, unseen data. For classification models, common metrics include accuracy, confusion matrix, precision, recall, F1 score, and AUC. For regression models, common metrics are mean absolute error, mean squared error, R2 score, and adjusted R2. The document provides formulas and explanations for calculating and interpreting each of these important performance metrics.
This document discusses performance metrics for evaluating machine learning models. It explains that performance metrics help understand how well a model performs on its training data and new, unseen data. For classification models, common metrics include accuracy, confusion matrix, precision, recall, F1 score, and AUC. For regression models, common metrics are mean absolute error, mean squared error, R2 score, and adjusted R2. The document provides formulas and explanations for calculating and interpreting each of these important performance metrics.
The document discusses the chi-square test of independence and provides examples of applying it. It first defines the chi-square test and explains that it determines if there is a significant relationship between two categorical variables. Then, it analyzes four problems using a chi-square test to assess relationships between variables like product purchased and customer gender, region and computer ownership, current and preferred smartphone brand, and alcohol drinking and smoking habits. The document demonstrates how to set up and interpret the results of chi-square tests, including observing frequencies, calculating test statistics, and determining if relationships are statistically significant.
Journal ArticleSales and Dealership Size as a Pred.docxcroysierkathey
Journal Article
Sales and Dealership Size as a Predictor of a Store’s Profit
Abstract
This study aims to know if a dealership’s size and sales could affect the owner’s profit. The statistical analysis that was used is multiple linear regression analysis. The results showed that a dealership’s size can explain 94.46% of the owner’s profit. On the other hand, the sales in both Sedans and SUV’s can explain 79.26% of the owner’s profit. Other than that, the analysis also showed that the increase in dealership size by a thousand sq. ft can also increase the profit by 11 940. For the sales, an increase in Sedan sales by one could increase the profit by 2 320 and an increase in SUV sales by one could increase the profit by 4 790. All of the coefficients and the regression models are proven significant and reliable by using multiple hypothesis testing. By using these results, a person aspiring to be a retailer owner would know what to increase so that his/her profits would increase too.
SALES AND DEALERSHIP SIZE AS A PREDICTOR OF A STORE’S PROFIT
Establishing a store is easy because all that is needed is an initial investment and good management skills. The challenging task to do is making that store successful. There are many factors that could affect a store’s monthly profit. The mere design of a retailer, including color and interior design, can increase the owner’s profit. One measurable factor that could affect revenue is the owner’s initial investment. If the owner is willing to risk a lot, then the possible income would be more than that. In the end, knowing how much one factor can affect a store’s profit is a desirable trait. It can be achieved easily by using regression analysis in Microsoft Excel or SPSS. Getting the data is easy but interpreting the data can be difficult.
METHODOLOGY
Linear regression and multiple linear regression analysis are both thorough methods of determining correlation and determination. This is the statistical analysis used. By using Microsoft Excel’s Analyst Tool Pack, summary outputs of regression statistics and ANOVA was able to be gathered. The summary outputs are attached in the appendices. From those analyses, the equations for the predicted value of profit based on the independent variables were created. Other than the equations, their characteristics are also present, such as the standard error, t-stat, p-value, and F value. Standard error of a statistic is the standard deviation of the data, which uses sampling distribution (Everett). In regression, it is the standard error of the regression coefficient. P-value is the probability value for a given statistical data is the same or greater than the number of the observed (Wasserstein and Lazar). F value is used to compare the data that has been fitted to another data set to check if the sample can represent the population (Lomax). Lastly, the t-statistic is the proportion of how far the value of a restriction is from a computed value to its stan ...
The document discusses linear regression analysis. It defines a regression equation as an equation that expresses the linear relationship between two variables. It explains that regression analysis uses the independent variable (X) to estimate the dependent variable (Y), and that the relationship is determined using the least squares method to minimize the difference between predicted and actual Y values. It provides an example of finding the regression equation relating number of sales calls to copiers sold.
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.
Linear regression is a statistical method used to explain the relationship between variables. The document discusses:
1) An agenda covering regression, diagnostics, differences between linear and logistic regression, assumptions, and interview questions.
2) Details on linear regression including understanding the algorithm, assumptions around linearity, normality, multicollinearity, autocorrelation, and homoscedasticity.
3) How to check if assumptions are violated including residual plots, Q-Q plots, and various statistical tests.
The document provides an in-depth overview of linear regression modeling, assumptions, and how to diagnose potential issues.
This chapter discusses various methods for describing and exploring quantitative data, including dot plots, stem-and-leaf displays, percentiles, box plots, measures of skewness, scatter diagrams, and contingency tables. It provides examples and explanations of how to construct and interpret each method. Key goals are to develop an understanding of distributions and relationships within data sets.
This document provides an overview of regression analysis, including:
- Regression analysis is used to study the relationship between variables and predict one variable from another. It can be linear or non-linear.
- Simple regression involves one independent and one dependent variable, while multiple regression involves two or more independent variables.
- The method of least squares is used to determine the regression equation that best fits the data by minimizing the sum of the squared residuals.
This overview discusses the predictive analytical technique known as Gradient Boosting Regression, an analytical technique that explore the relationship between two or more variables (X, and Y). Its analytical output identifies important factors ( Xi ) impacting the dependent variable (y) and the nature of the relationship between each of these factors and the dependent variable. Gradient Boosting Regression is limited to predicting numeric output so the dependent variable has to be numeric in nature. The minimum sample size is 20 cases per independent variable. The Gradient Boosting Regression technique is useful in many applications, e.g., targeted sales strategies by using appropriate predictors to ensure accuracy of marketing campaigns and clarify relationships among factors such as seasonality, product pricing and product promotions, or for an agriculture business attempting to ascertain the effects of temperature, rainfall and humidity on crop production. Gradient Boosting Regression is just one of the numerous predictive analytical techniques and algorithms included in the Assisted Predictive Modeling module of the Smarten augmented analytics solution. This solution is designed to serve business users with sophisticated tools that are easy to use and require no data science or technical skills. Smarten is a representative vendor in multiple Gartner reports including the Gartner Modern BI and Analytics Platform report and the Gartner Magic Quadrant for Business Intelligence and Analytics Platforms Report.
STATATHON: Unleashing the Power of Statistics in a 48-Hour Knowledge Extravag...sameer shah
"Join us for STATATHON, a dynamic 2-day event dedicated to exploring statistical knowledge and its real-world applications. From theory to practice, participants engage in intensive learning sessions, workshops, and challenges, fostering a deeper understanding of statistical methodologies and their significance in various fields."
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Data and AI
Round table discussion of vector databases, unstructured data, ai, big data, real-time, robots and Milvus.
A lively discussion with NJ Gen AI Meetup Lead, Prasad and Procure.FYI's Co-Found
State of Artificial intelligence Report 2023kuntobimo2016
Artificial intelligence (AI) is a multidisciplinary field of science and engineering whose goal is to create intelligent machines.
We believe that AI will be a force multiplier on technological progress in our increasingly digital, data-driven world. This is because everything around us today, ranging from culture to consumer products, is a product of intelligence.
The State of AI Report is now in its sixth year. Consider this report as a compilation of the most interesting things we’ve seen with a goal of triggering an informed conversation about the state of AI and its implication for the future.
We consider the following key dimensions in our report:
Research: Technology breakthroughs and their capabilities.
Industry: Areas of commercial application for AI and its business impact.
Politics: Regulation of AI, its economic implications and the evolving geopolitics of AI.
Safety: Identifying and mitigating catastrophic risks that highly-capable future AI systems could pose to us.
Predictions: What we believe will happen in the next 12 months and a 2022 performance review to keep us honest.
Codeless Generative AI Pipelines
(GenAI with Milvus)
https://ml.dssconf.pl/user.html#!/lecture/DSSML24-041a/rate
Discover the potential of real-time streaming in the context of GenAI as we delve into the intricacies of Apache NiFi and its capabilities. Learn how this tool can significantly simplify the data engineering workflow for GenAI applications, allowing you to focus on the creative aspects rather than the technical complexities. I will guide you through practical examples and use cases, showing the impact of automation on prompt building. From data ingestion to transformation and delivery, witness how Apache NiFi streamlines the entire pipeline, ensuring a smooth and hassle-free experience.
Timothy Spann
https://www.youtube.com/@FLaNK-Stack
https://medium.com/@tspann
https://www.datainmotion.dev/
milvus, unstructured data, vector database, zilliz, cloud, vectors, python, deep learning, generative ai, genai, nifi, kafka, flink, streaming, iot, edge
Analysis insight about a Flyball dog competition team's performanceroli9797
Insight of my analysis about a Flyball dog competition team's last year performance. Find more: https://github.com/rolandnagy-ds/flyball_race_analysis/tree/main
ViewShift: Hassle-free Dynamic Policy Enforcement for Every Data LakeWalaa Eldin Moustafa
Dynamic policy enforcement is becoming an increasingly important topic in today’s world where data privacy and compliance is a top priority for companies, individuals, and regulators alike. In these slides, we discuss how LinkedIn implements a powerful dynamic policy enforcement engine, called ViewShift, and integrates it within its data lake. We show the query engine architecture and how catalog implementations can automatically route table resolutions to compliance-enforcing SQL views. Such views have a set of very interesting properties: (1) They are auto-generated from declarative data annotations. (2) They respect user-level consent and preferences (3) They are context-aware, encoding a different set of transformations for different use cases (4) They are portable; while the SQL logic is only implemented in one SQL dialect, it is accessible in all engines.
#SQL #Views #Privacy #Compliance #DataLake
Learn SQL from basic queries to Advance queriesmanishkhaire30
Dive into the world of data analysis with our comprehensive guide on mastering SQL! This presentation offers a practical approach to learning SQL, focusing on real-world applications and hands-on practice. Whether you're a beginner or looking to sharpen your skills, this guide provides the tools you need to extract, analyze, and interpret data effectively.
Key Highlights:
Foundations of SQL: Understand the basics of SQL, including data retrieval, filtering, and aggregation.
Advanced Queries: Learn to craft complex queries to uncover deep insights from your data.
Data Trends and Patterns: Discover how to identify and interpret trends and patterns in your datasets.
Practical Examples: Follow step-by-step examples to apply SQL techniques in real-world scenarios.
Actionable Insights: Gain the skills to derive actionable insights that drive informed decision-making.
Join us on this journey to enhance your data analysis capabilities and unlock the full potential of SQL. Perfect for data enthusiasts, analysts, and anyone eager to harness the power of data!
#DataAnalysis #SQL #LearningSQL #DataInsights #DataScience #Analytics
2. 2
GOALS
● Understand and interpret the terms dependent and
independent variable.
● Calculate and interpret the coefficient of correlation,
the coefficient of determination, and the standard
error of estimate.
● Conduct a test of hypothesis to determine whether
the coefficient of correlation in the population is zero.
● Calculate the least squares regression line.
● Construct and interpret confidence and prediction
intervals for the dependent variable.
3. 3
Regression Analysis - Introduction
● Recall in Chapter 4 the idea of showing the
relationship between two variables with a scatter
diagram was introduced.
● In that case we showed that, as the age of the buyer
increased, the amount spent for the vehicle also
increased.
● In this chapter we carry this idea further. Numerical
measures to express the strength of relationship
between two variables are developed.
● In addition, an equation is used to express the
relationship. between variables, allowing us to
estimate one variable on the basis of another.
4. 4
Regression Analysis - Uses
Some examples.
● Is there a relationship between the amount
Healthtex spends per month on advertising and its
sales in the month?
● Can we base an estimate of the cost to heat a home
in January on the number of square feet in the
home?
● Is there a relationship between the miles per gallon
achieved by large pickup trucks and the size of the
engine?
● Is there a relationship between the number of hours
that students studied for an exam and the score
earned?
5. 5
Correlation Analysis
● Correlation Analysis is the study of the
relationship between variables. It is also
defined as group of techniques to measure
the association between two variables.
● A Scatter Diagram is a chart that portrays
the relationship between the two variables.
It is the usual first step in correlations
analysis
– The Dependent Variable is the variable being
predicted or estimated.
– The Independent Variable provides the basis for
estimation. It is the predictor variable.
6. 6
Regression Example
The sales manager of Copier
Sales of America, which has a
large sales force throughout
the United States and Canada,
wants to determine whether
there is a relationship between
the number of sales calls made
in a month and the number of
copiers sold that month. The
manager selects a random
sample of 10 representatives
and determines the number of
sales calls each representative
made last month and the
number of copiers sold.
8. 8
The Coefficient of Correlation, r
The Coefficient of Correlation (r) is a measure of the
strength of the relationship between two variables. It
requires interval or ratio-scaled data.
● It can range from -1.00 to 1.00.
● Values of -1.00 or 1.00 indicate perfect and strong
correlation.
● Values close to 0.0 indicate weak correlation.
● Negative values indicate an inverse relationship and
positive values indicate a direct relationship.
13. 13
Coefficient of Determination
The coefficient of determination (r2
) is the
proportion of the total variation in the
dependent variable (Y) that is explained or
accounted for by the variation in the
independent variable (X). It is the square
of the coefficient of correlation.
● It ranges from 0 to 1.
● It does not give any information on the
direction of the relationship between the
variables.
14. 14
Using the Copier Sales of
America data which a
scatterplot was
developed earlier,
compute the
correlation coefficient
and coefficient of
determination.
Correlation Coefficient - Example
17. 17
How do we interpret a correlation of 0.759?
First, it is positive, so we see there is a direct relationship between
the number of sales calls and the number of copiers sold. The
value of 0.759 is fairly close to 1.00, so we conclude that the
association is strong.
However, does this mean that more sales calls cause more sales?
No, we have not demonstrated cause and effect here, only that the
two variables—sales calls and copiers sold—are related.
Correlation Coefficient - Example
18. 18
Coefficient of Determination (r2
) - Example
• The coefficient of determination, r2
,is 0.576,
found by (0.759)2
• This is a proportion or a percent; we can say that
57.6 percent of the variation in the number of
copiers sold is explained, or accounted for, by the
variation in the number of sales calls.
19. 19
Testing the Significance of
the Correlation Coefficient
H0: ρ = 0 (the correlation in the population is 0)
H1: ρ ≠ 0 (the correlation in the population is not 0)
Reject H0 if:
t > tα/2,n-2 or t < -tα/2,n-2
20. 20
Testing the Significance of
the Correlation Coefficient - Example
H0: ρ = 0 (the correlation in the population is 0)
H1: ρ ≠ 0 (the correlation in the population is not 0)
Reject H0 if:
t > tα/2,n-2 or t < -tα/2,n-2
t > t0.025,8 or t < -t0.025,8
t > 2.306 or t < -2.306
21. 21
Testing the Significance of
the Correlation Coefficient - Example
The computed t (3.297) is within the rejection region, therefore, we will reject H0. This means
the correlation in the population is not zero. From a practical standpoint, it indicates to
the sales manager that there is correlation with respect to the number of sales calls
made and the number of copiers sold in the population of salespeople.
26. 26
Regression Analysis
In regression analysis we use the independent variable
(X) to estimate the dependent variable (Y).
● The relationship between the variables is linear.
● Both variables must be at least interval scale.
● The least squares criterion is used to determine the
equation.
27. 27
Regression Analysis – Least Squares
Principle
● The least squares principle is used to
obtain a and b.
● The equations to determine a and b
are:
29. 29
Regression Equation - Example
Recall the example involving
Copier Sales of America. The
sales manager gathered
information on the number of
sales calls made and the
number of copiers sold for a
random sample of 10 sales
representatives. Use the least
squares method to determine a
linear equation to express the
relationship between the two
variables.
What is the expected number of
copiers sold by a
representative who made 20
calls?
33. 33
The Standard Error of Estimate
● The standard error of estimate measures the
scatter, or dispersion, of the observed values
around the line of regression
● The formulas that are used to compute the
standard error:
34. 34
Standard Error of the Estimate - Example
Recall the example
involving Copier Sales of
America. The sales
manager determined the
least squares regression
equation is given below.
Determine the standard
error of estimate as a
measure of how well the
values fit the regression
line.
37. 37
Assumptions Underlying Linear
Regression
For each value of X, there is a group of Y values, and these
● Y values are normally distributed. The means of these normal
distributions of Y values all lie on the straight line of regression.
● The standard deviations of these normal distributions are equal.
● The Y values are statistically independent. This means that in
the selection of a sample, the Y values chosen for a particular X
value do not depend on the Y values for any other X values.
38. 38
Confidence Interval and Prediction
Interval Estimates of Y
• A confidence interval reports the mean value of Y
for a given X.
• A prediction interval reports the range of values
of Y for a particular value of X.
39. 39
Confidence Interval Estimate - Example
We return to the Copier Sales of America
illustration. Determine a 95 percent confidence
interval for all sales representatives who make
25 calls.
40. 40
Step 1 – Compute the point estimate of Y
In other words, determine the number of copiers we expect a
sales representative to sell if he or she makes 25 calls.
Confidence Interval Estimate - Example
41. 41
Step 2 – Find the value of t
● To find the t value, we need to first know the number
of degrees of freedom. In this case the degrees of
freedom is n - 2 = 10 – 2 = 8.
● We set the confidence level at 95 percent. To find
the value of t, move down the left-hand column of
Appendix B.2 to 8 degrees of freedom, then move
across to the column with the 95 percent level of
confidence.
● The value of t is 2.306.
Confidence Interval Estimate - Example
43. 43
Confidence Interval Estimate - Example
Step 4 – Use the formula above by substituting the numbers
computed
in previous slides
Thus, the 95 percent confidence interval for the average sales of all
sales representatives who make 25 calls is from 40.9170 up to
56.1882 copiers.
44. 44
Prediction Interval Estimate - Example
We return to the Copier Sales of America
illustration. Determine a 95 percent
prediction interval for Sheila Baker, a West
Coast sales representative who made 25
calls.
45. 45
Step 1 – Compute the point estimate of Y
In other words, determine the number of copiers we
expect a sales representative to sell if he or she
makes 25 calls.
Prediction Interval Estimate - Example
46. 46
Step 2 – Using the information computed
earlier in the confidence interval estimation
example, use the formula above.
Prediction Interval Estimate - Example
If Sheila Baker makes 25 sales calls, the number of copiers she
will sell will be between about 24 and 73 copiers.
48. 48
Transforming Data
● The coefficient of correlation describes the
strength of the linear relationship between
two variables. It could be that two variables
are closely related, but there relationship is
not linear.
● Be cautious when you are interpreting the
coefficient of correlation. A value of r may
indicate there is no linear relationship, but it
could be there is a relationship of some
other nonlinear or curvilinear form.
49. 49
Transforming Data - Example
On the right is a listing of 22
professional golfers, the number of
events in which they participated,
the amount of their winnings, and
their mean score for the 2004
season. In golf, the objective is to
play 18 holes in the least number of
strokes. So, we would expect that
those golfers with the lower mean
scores would have the larger
winnings. To put it another way,
score and winnings should be
inversely related. In 2004 Tiger
Woods played in 19 events, earned
$5,365,472, and had a mean score
per round of 69.04. Fred Couples
played in 16 events, earned
$1,396,109, and had a mean score
per round of 70.92. The data for the
22 golfers follows.
50. 50
Scatterplot of Golf Data
● The correlation between the
variables Winnings and
Score is 0.782. This is a
fairly strong inverse
relationship.
● However, when we plot the
data on a scatter diagram
the relationship does not
appear to be linear; it does
not seem to follow a straight
line.
51. 51
What can we do to explore other (nonlinear)
relationships?
One possibility is to transform one of the
variables. For example, instead of using Y
as the dependent variable, we might use its
log, reciprocal, square, or square root.
Another possibility is to transform the
independent variable in the same way.
There are other transformations, but these
are the most common.
52. 52
In the golf winnings
example, changing the
scale of the dependent
variable is effective. We
determine the log of
each golfer’s winnings
and then find the
correlation between the
log of winnings and
score. That is, we find
the log to the base 10 of
Tiger Woods’ earnings of
$5,365,472, which is
6.72961.
Transforming Data - Example
55. 55
Using the Transformed Equation for
Estimation
Based on the regression equation, a golfer
with a mean score of 70 could expect to
earn:
• The value 6.4372 is the log to the base 10 of winnings.
• The antilog of 6.4372 is 2.736
• So a golfer that had a mean score of 70 could expect to
earn $2,736,528.