MGT 6203 Midterm Test Questions with Correct Answers Latest Update

MGT 6203 Midterm Test Questions with Correct Answers Latest Update How does the skew of a distribution affect its median relative to its mean? - Answers Left skewed -> mean < median No skew -> mean = median Right skew -> mean > median Define correlation coefficient - Answers Correlation coefficient captures strength of linear relationships Define total deviation, explained deviation, and unexplained deviation for OLS linear regression problem. - Answers Total deviation: difference between observation and mean Explained deviation: difference between predicted value and mean Unexplained deviation/ error/residual: difference between predicted value and observed value Define total sum of squares (SST), sum of squared errors (SSE), and sum of squares regression (SSR) and how they relate to one another. - Answers SST = (observation - average)^2 SSE = (observation - prediction)^2 SSR = (average - prediction)^2 SST = SSE + SSR Define R^2 and adjusted R^2 - Answers R^2 = 1- (SSE)/(SST) = SSR/SST R^2 = explained deviation/ total deviation, a measure of overall strength between dependent and independent variables Adjusted R^2 adds a penalty based on the number of independent variables (p) and observations (n) Adjusted R^2 = 1 - SSE*(n-1)/(SST * (n-p-1)) What values can R^2 occupy? How does one interpret the value of R^2? - Answers 0 <= R^2 <= 1 R^2 = 1: X accounts for all Y variation R^2 = 0: X accounts for none of the Y variation Explain T-value, P-value and F-statistic - Answers Null hypothesis (H_0): coefficient is 0 T-value = coefficient estimate divided by its standard error P-value: null hypothesis that T-value = (what is the probability that null hypothesis true?) --> reject if low probability F-statistic: probability that coefficient is 0 How do you compute the F-statistic - Answers F-statistic = {(SSR/P)}/{(SSE)/(N-P-1)} How does R^2 change as a factor of number of variables? - Answers R^2 will either increase or stay the same as you add more variables. What are the 3 main assumptions of linear regression? - Answers 1. Linear assumption: Value of Y at each value of X approximates a straight line 2. Assumption about errors: The error terms are independently and identically distributed normal random variables, each with mean 0 and constant variance (homoscedasticity) 3. Assumptions about predictors: In multiple regression, predictor variables are assumed to be linearly independent of one another. What are the 6 most common problems in fitting linear regression? - Answers 1. Non-linearity of response predictor relationship 2. Correlation of error terms 3. Non-constant variance of error terms 4. Outliers 5. High-leverage points 6. Collinearity How can you identify if a relationship is nonlinear? If it is, how can you address it? - Answers Identify by plotting the two variables against one another (should see a line) or plotting residuals vs. fitted values (want to see no patterns) If the relationship is nonlinear, you can transform the variables (using a higher order term or log), look for outliers, see if you are missing a variable, or check for systematic bias. How can one detect autocorrelations of error terms? What are the effects of autocorrelation of error terms? - Answers Detection: Durbin-Watson test Effects of autocorrelation of error terms: § Estimated standard errors will underestimate true standard errors § Confidence and prediction intervals will be narrower than they should be and p-values will be lower than they should be § Sense of confidence in model that is not warranted How can one detect heteroskedasticity (non-constant error variance)? What are the effects of non-constant error terms? How can you handle it? - Answers Detection: Residuals vs. fitted plots --> if non-constant, points to heteroskedasticity Effects: Hypotheses tests and confidence intervals may be misleading Treatment: Transform Y variable (ln(Y), 1/Y, etc. How can you detect outliers? How should you handle them? - Answers Detection: Plot residuals (or standardized residuals) against predicted values of y Handling: Do not assume that an outlier observation should be removed à may signal a model