MGT 6203 MIDTERM EXAM UPDATED
QUESTIONS AND CORRECT ANSWERS.
How does the skew of a distribution affect its median relative to its mean? - ANS Left skewed
-> mean < median
No skew -> mean = median
Right skew -> mean > median
Define correlation coefficient - ANS Correlation coefficient captures strength of linear
relationships
Define total deviation, explained deviation, and unexplained deviation for OLS linear regression
problem. - ANS 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. - ANS SST = (observation - average)^2
SSE = (observation - prediction)^2
SSR = (average - prediction)^2
SST = SSE + SSR
Define R^2 and adjusted R^2 - ANS R^2 = 1- (SSE)/(SST) = SSR/SST
1 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED
, 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? - ANS 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 - ANS 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 - ANS F-statistic = {(SSR/P)}/{(SSE)/(N-P-1)}
How does R^2 change as a factor of number of variables? - ANS R^2 will either increase or
stay the same as you add more variables.
What are the 3 main assumptions of linear regression? - ANS 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.
2 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED
QUESTIONS AND CORRECT ANSWERS.
How does the skew of a distribution affect its median relative to its mean? - ANS Left skewed
-> mean < median
No skew -> mean = median
Right skew -> mean > median
Define correlation coefficient - ANS Correlation coefficient captures strength of linear
relationships
Define total deviation, explained deviation, and unexplained deviation for OLS linear regression
problem. - ANS 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. - ANS SST = (observation - average)^2
SSE = (observation - prediction)^2
SSR = (average - prediction)^2
SST = SSE + SSR
Define R^2 and adjusted R^2 - ANS R^2 = 1- (SSE)/(SST) = SSR/SST
1 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED
, 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? - ANS 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 - ANS 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 - ANS F-statistic = {(SSR/P)}/{(SSE)/(N-P-1)}
How does R^2 change as a factor of number of variables? - ANS R^2 will either increase or
stay the same as you add more variables.
What are the 3 main assumptions of linear regression? - ANS 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.
2 @COPYRIGHT 2025/2026 ALLRIGHTS RESERVED
