Regression (ISYE 6414) - Module 1 Exam Questions and Answers Already Passed Latest Update

Regression (ISYE 6414) - Module 1 Exam Questions and Answers Already Passed Latest Update Regression modeling - Answers a modeling technique that we use to analyze and estimate the values of a response variable by using other variables that it's correlated with Response Variable - Answers the dependent variable, represented by Y variable we are interested in modeling in experimental/observational studies we observe the response and have observations of the response random variable a random variable that varies with changes in the predictors along with other random changes Predicting Variable - Answers explanatory variable, independent variable, represented by X variables we think might be useful in predicting/modeling the response variables a fixed variable does not change with the response, we set the predicting variables before the response is measured 3 objectives of regression - Answers 1) prediction of the response, see how the response variable behaves in different settings 2) modeling the relationship between the response variable and explanatory variables 3) testing hypotheses of association relationship Benefits of linear models - Answers simple to understand simple mathematically works well for a wide variety of circumstances not a true representation of reality but a useful representation of reality What is the goal of simple linear regression? - Answers find the best line that describes a linear relationship/ find the line that fits the data What are the 4 assumptions of simple linear regression? - Answers 1) linearity - the expectation of the deviation (error) is 0 2) constant variance - variance of error terms/deviances is constant 3) Independence - deviances (errors) are independent random variables 4) normality - needed for statistical inference like confidence and hypothesis testing How do you test the constant variance assumption in simple linear regression? - Answers Create a scatter plot of the residuals plotted against the fitted values if the points are not randomly spread out (closer together in some areas and more spread out in others) there may not be constant variance What does violation of the constant variance assumption result in for simple linear regression? - Answers the estimates are not as efficient as they could be in estimating the true parameters and poorly calibrated prediction intervals How do you test the linearity assumption in simple linear regression? - Answers Create a scatter plot of the data. if a line does not appear to be a good fit for the data (maybe the data is curved or has an asymptote) the relationship between x and y may not be linear Create a scatter plot of residuals plotted against the fitted values. If the residuals do not appear to be random and constant around the ideal baseline the relationship between x and y may not be linear What does violation of the linearity assumption result in for simple linear regression? - Answers difficulties estimating beta_0 (intercept) and model does not include a necessary systematic component How do you test the independence assumption in simple linear regression? - Answers You cannot test the independence assumption easily. It would involve looking at every transformation of the data for correlation. Instead you test the correlation by creating a scatter plot of the residuals plotted against the fitted values if there are clusters of residuals the independence assumption may not hold. If there aren't clusters of residuals you still cannot say for sure the independence assumption holds What does violation of the independence assumption result in for simple linear regression? - Answers often occurs in data that are ordered in time and can lead to misleading assessments of the strength of the regression How do you test the normality assumption in simple linear regression? - Answers create a QQ plot - a straight line on the plot indicates the assumption holds, curvature (especially at the ends) indicates it may not hold