ISYE 6414 Exam Questions Answered Correctly Latest Update (Graded A+)

ISYE 6414 Exam Questions Answered Correctly Latest Update (Graded A+) Which variable type is considered "random"? - Answers response variable - it varies with changes in the predicting variables Which variable type is considered "fixed"? - Answers predicting variables- the predicting variables are set before the response variable is measured A regression model tries to explain/predict the ___ of the response variable by using the predicting variables (x). Some explained by x and some due to ____. - Answers (1) total variability, (2) random error What are the 3 objectives in regression? - Answers (1) Prediction- predicting how the response variable behaves in different settings (2) Modeling the relationship (3) Testing hypotheses of association relationships Y = β0 + β1x + ε - Answers Simple linear regression equation What is β1 in the simple linear regression equation? - Answers Slope. The expected (average) change in Y associated with a 1- unit increase in the value of x. What is β0 in the simple linear regression equation? - Answers Intercept. The average value of Y when x is zero. What is ε in the simple linear regression equation? - Answers Deviance/error Define what it means for a model to be non-deterministic? - Answers the outcome cannot be predicted with certainty, even if the inputs are known. The model behaves differently each time it is run Is ε considered random or fixed? - Answers random What are the assumptions of a simple linear regression model? - Answers (1) linearity/mean zero assumption (2) constant variance assumption (3) Independence assumption (4) Normal distribution of error terms Assumption of linearity - Answers Expectation of the deviances is 0 Assumption of constant variance - Answers The variance (σ2) of the error terms (ε) is constant for the given population Assumption of independence - Answers Deviances (ε) are independent, random variables T or F: Parameters β1, β0, and ε in statistical modeling are observed in the data and therefore fixed, known quantities. - Answers False. These parameters are considered unknown regardless of how much data is observed. Approximate values are estimated. In simple linear regression, the fitted line ____. - Answers makes the errors as small as possible given a criterion (function of error terms) To estimate β1 and β0, we find values that minimize the ___. - Answers sum of squared residuals or errors. or in other words: total squared deviances from the line What does the "hat" ("^") symbolize? - Answers Differentiates estimated parameters from the true, unknown values Median or robust regression - Answers Replace squared error criterion used in the standard regression model with the absolute value of errors Sxx, Sxy and Syy - Answers Sum of Square terms Define what it means for a model to be deterministic? - Answers Given the same input values, the model will consistently return the same output Residual - Answers difference between the observed and fitted values Mean squared error (MSE) in SLR - Answers Sum of the squared residuals divided by n-2 SSE/(n-2) What is the sampling distribution of the estimator of the variance parameter in SLR? - Answers Chi-square with n-2 degrees of freedom sample variance estimator equation - Answers sum of the Zi minus their average, squared, divided by n-1 Σxi yi - (Σxi )(Σyi )/n - Answers Sxy Σxi^2 - (Σxi )^2/n - Answers Sxx When β1 is positive, it is consistent with a ___ relationship between x and y. - Answers direct When β1 is negative it is consistent with a ___ relationship between x and y. - Answers inverse When β1 is close to 0, it is consistent with a ___ relationship between x and y. - Answers insignificant How do you find the variance from residual standard error? - Answers take the square of the residual standard error (also called the standard deviation of the error terms) Define extrapolation. - Answers When the regression equation is used to produce a y value from an x value that is outside the range of the observed x values Why does the MSE divide by (n-2) instead of (n-1)? - Answers an additional degree of freedom is lost because both β0 and β1 are estimates Define unbiasedness - Answers The expectation that the parameter's estimated value is exactly the true value T or F: β1 hat is normally distributed - Answers True. β1 hat is a linear combination of normally distributed variables and thus is also normally distributed. β1 hat is a ___ distribution with ___ degrees of freedom - Answers (1) t (2) n-2 Data points that are far from the mean of the x's - Answers leverage points Data point that is far from the mean of the x's and/or y's - Answers influential point When do you use adjusted R-squared? - Answers when comparing models When do you use R-squared? - Answers when evaluating the model performance in terms of variability explained Box-Cox Transformation - Answers a power transformation of y that normalizes or variance-stablizes the response variable What is overarching objective of ANOVA? - Answers Compare the means across k number of populations in ANOVA, we compare the ___ to the ___of the response data - Answers (1) within-variability (2) between variability The only difference in assumptions from the linear regression model is the ___ assumption not needed in ANOVA. - Answers linearity Do you use ANOVA or linear regression when the predicting factor is either a categorical or qualitative variable? - Answers ANOVA degree of freedom in the estimation in the pooled variance estimator - Answers N-k MSE = SSE/N-k - Answers within-group variability MSST= SSTr/k-1 - Answers between-group variability