ISYE 6414 REGRESSION MIDTERM 1 EXAM 2024 / ISYE6414 MIDTERM 1 REAL EXAM QUESTIONS AND 100% CORRECT ANSWERS/ A+ GUARANTEED

What are the variables in regression? -CORRECT ANSWER- 1. Response (dependent) variable - one particular variable that we are interested in understanding or modelling, such as sales of a particular product. 2. Predicting or Explanatory (independent) variable - set of other variables that we think might be useful in predicting or modelling the response variable (like the price of a product) Which regression variable is a Random variable? -CORRECT ANSWER-- Response Variable - It varies with changes in the predictor along with other random changes Which regression variable is a Fixed variable? -CORRECT ANSWER-- Predicting Variable - It does not change with the response but it is set fixed before the response is measured. What are the objectives in regression analysis? -CORRECT ANSWER-- 1. Prediction - of the response variable 2. Modelling - the relationship between the response variable and the explanatory variables 3. Testing - hypotheses of association relationships. What are the given assumptions when building a linear regression model? - CORRECT ANSWER-- 1. Linearity/Mean Zero Assumption - it cannot be true that for certain subgroups in the population, the model is consistently too low, while for others, it's consistently too high. 2. 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. 3. Independence Assumption are independent random variables - it cannot be true knowing that the model under-predicts y for one particular case tells you anything or all about what it does for any other case. (her language) 4. Normally distributed. What is the value that is being optimized towards in a linear regression problem? - CORRECT ANSWER-- Minimizing the sum of squared errors In terms of model parameter interpretation, how would you interpret a positive value for B1, negative value, and value close to 0? -CORRECT ANSWER-- A positive value of B1 is consistent with a direct relationship between x and y A negative value of B1 is consistent with an inverse relationship between x and y A close to zero value of B1 means that there is not a significant association between x and y What are the interpretations of the Least Squares estimated coefficients (B hat 1 and B hat 0) -CORRECT ANSWER-- B hat 1 is the estimated expected change in the response variable associated with the unit of change in the predicting variable B hat 0 is the estimated expected value of the response variable when the predicting variable equals zero What is extrapolation? -CORRECT ANSWER-- When you try to predict a value using your regression model that is outside of the observed range. It is unreliable to use extrapolation. Assuming that the data are normally distributed, under the simple linear model, the estimated variance has the following sample distribution: A) Chi-square with n-2 degrees of freedom B) T-distribution with n-2 degrees of freedom C) Chi-square with n degrees of freedom D) T-distribution with n degrees of freedom -CORRECT ANSWER-- A) Chi- square with n-2 degrees of freedom The fitted values are defined as: A) The difference between observed and expected responses B) The regression line with parameters replaced with the estimated regression coefficients C) The regression line D) The response values. -CORRECT ANSWER-- B) The regression line with parameters replaced with the estimated regression coefficients. The estimators of the linear regression model are derived by: A) Minimizing the sum of squared differences between observed and expected values of the response variable. B) Maximizing the sum of squared differences between observed and expected values of the response variable. C) Minimizing the sum of absolute differences between observed and expected values of the response variable. D) Maximizing the sum of absolute differences between observed and expected values of the response variable. -CORRECT ANSWER-- A) Minimizing the sum of squared differences between observed and expected values of the response variable. When using the t-test for statistical significance, when would you interpret B1 as statistically significant? -CORRECT ANSWER-- We reject the null hypothesis of the absolute value of the t-value is large. If the null hypothesis is rejected, we interpret this as B1 being statistically significant. What is statistical significance? -CORRECT ANSWER-- It means that B1 is statistically different from zero. When using the p-value test for statistical significance, when would you interpret B1 as statistically significant? -CORRECT ANSWER-- If the P-value is small (.01) then we would reject the null hypothesis and determine that B1 is statistically significant. What is the p-value? -CORRECT ANSWER-- The p-value is a measure of how reject-able the null hypothesis is. The smaller the p-value, the more reject-able the null hypothesis is for the observed data. The estimators for the regression coefficients are: A) Biased but with small variance