Introduction to Regression Analysis von Edu Pristine

Dozent des Vortrages Introduction to Regression Analysis

Edu Pristine

Trusted by Fortune 500 Companies and 10,000 Students from 40+ countries across the globe, EduPristine is one of the leading International Training providers for Finance Certifications like FRM®, CFA®, PRM®, Business Analytics, HR Analytics, Financial Modeling, Operational Risk Modeling etc. It was founded by industry professionals who have worked in the area of investment banking and private equity in organizations such as Goldman Sachs, Crisil - A Standard & Poors Company, Standard Chartered and Accenture.

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... one independent variable. Explain the impact of changes in an independent variable on the dependent variable "Dependent variable: the variable we wish to explain "Independent variable: the variable used to explain the dependent variable ...

... function "Changes in y are assumed to be caused by changes ...

... Negative Linear Relationship Relationship NOT Linear ...

... Knowledge Management Pristine1 Random Error for this x value X Predicted Value of Y for Xi xi Slope = ...

... residual Dependent Variable Independent Variable ...

... actual y values as compared the predicted y values from the Sample Regression Line "It would be good if we were able to reduce this error term "What are we trying to achieve by Sample Regression? ...

... values of b 0 and b 1 that minimize the sum of the squared residuals ...

... Pristine9 "The sum of the residuals from the least squares regression line is 0 "The sum of the squared residuals is a minimum Minimize( ) "The simple regression line always passes through the mean of ...

... change in x Interpretation of the Slope and the Intercept ...

... the explanatory variable X "Error values are normally distributed for any given value of X "The probability distribution of the errors for different X has constant variance (homoscedacity) "Error values u for given X are statistically independent, their covariance is zero Pristine12 "The underlying relationship between the X variable and the Y ...

... independent variables in the model Pristine13 where SSE= Sum of Squares of Errors (summation of e 2 ) n = Sample size k ...

... from different possible samples ...

... H 0: ? 1= 0 (no linear relationship)H 1: ? 1"` 0 (linear relationship does exist) "Test statistic Pristine16 "t-test for a population slope. Is there a linear relationship ...

... Perfect linear relationship between x and y 100% of the variation in y is explained by variation in x ...

... Values (Cont &) Pristine x y x Weaker linear relationship between x and y ...

... Pristine9 Paul Graham, PRM is analyzing the sales growth of a baby product launched five years ago by a regional company. He assesses that three factors contribute heavily towards the growth and comes up with the following results: Y = b + 1.5 X 1+ 1.2X 2+ 3X ...

... the linear relationship (continued) Pristine13 "The population correlation coefficient (rho) measures the strength of the association between the variables "The sample correlation coefficient r is an estimate of ? and is used to measure the strength of the linear relationship in the sample observations "Features of ? and r ...

... Sample correlation coefficient or the algebraic equivalent Pristine15 where r = Sample correlation coefficient n = Sample size x = Value of the independent variable y = Value of the dependent variable ...