ISYE 6414 - All Units Latest Update Graded A

ISYE 6414 - All Units Latest Update Graded A response (dependent) variables one particular variable that we are interested in understanding or modeling (y) predicting or explanatory (independent) variables a set of other variables that might be useful in predicting or modeling the response variable (x1, x2) What kind of variable is a response variable and why? random, because it varies with changes in the predictor/s along with other random changes. What kind of variable is a predicting variable and why? fixed, because it does not change with the response but it is fixed before the response is measured. linear relationship a simple deterministic relationship between 2 factors, x and y what are three things that a regression analysis is used for? 1. Prediction of the response variable, 2. Modeling the relationship between the response and explanatory variables, 3. Testing hypotheses of association relationships B0 = ? intercept B1 = ? slope for our linear model where: Y = B0 + B1 + EPSILON (E), what does the epsilon represent? deviance of the data from the linear model (error term) what are the 4 assumptions of linear regression? Linearity/Mean Zero, Constant Variance, Independence, Normality Linearity/Mean zero assumption Means that the expected value (deviances) of errors is zero. This leads to difficulties in estimating B0 and means that our model does not include a necessary systematic component Constant variance assumption Means that it cannot be true that the model is more accurate for some parts of the population, and less accurate for other parts of the populations. This can result in less accurate parameters and poorly-calibrated prediction intervals. Assumption of Independence Means that the deviances, or in fact the response variables ys, are independently drawn from the data-generating process. (this most often occurs in time series data) This can result in very misleading assessments of the strength of regression. Normality assumption This is needed if we want to do any confidence or prediction intervals, or hypothesis test, which we usually do. If this assumption is violated, hypothesis test and confidence and prediction intervals and be very misleading. what are the 3 parameters we estimated in regression? B0, B1, sigma squared (variance of the one pop.) What do we mean by model parameters in statistics? Model parameters are unknown quantities, and they stay unknown regardless how much data are observed. We estimate those parameters given the model assumptions and the data, but through estimation, we're not identifying the true parameters. We're just estimating approximations of those parameters. What is the estimated sampling distribution of s^2? chi-square with n-1 DF Why do we lose 1 DF for s^2? we replace mu with zbar what is the relationship between s^2 and sigma^2? S^2 estimates sigma^2 What is the estimated sampling distribution of sigma^2? chi-square with n-2 DF (~ equivalent to MSE) Why do we lose 2 DF for sigma^2? we replaced two parameters, B0 and B1 In SLR, we are interested in the behavior of which parameter? B1 If we have a positive value for B1,.... then that's consistent with a direct relationship between the predicting variable x and the response variable y. If we have a negative value for B1,.... is consistent with a