STAT310 EXAM TERMINOLOGY QUESTIONS AND CORRECT DETAILED ANSWERS (VERIFIED ANSWERS) ||ALREADY GRADED A+||NEWEST VERSION

STAT310 EXAM TERMINOLOGY QUESTIONS
AND CORRECT DETAILED ANSWERS (VERIFIED
ANSWERS) ||ALREADY GRADED A+||NEWEST
VERSION
Quiz: How are parameters estimated for linear regression?

Ans: Method of least squares



Quiz: What is the multiple linear regression model?

Ans: Yi = B0 + B1Xi1 + ... + BpXip + ei



ei are random errors

Yi is the response for the ith case

There are p predictor variables x1, x2, ..., xp



Quiz: Least square estimates

Ans: Minimizes sum of squares



Quiz: Residual




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, Ans: Actual - Predicted value



Quiz: Residual sum of squares

Ans: sum of residuals squared (Yi - mu hat)^2 summed together



We want small RSS to indicate a better model (minimize SS)



Quiz: Factor

Ans: Is a categorical variable that can be incorporated into regression models
by dummy variables. Factors with k levels are coded with k-1 variables since one
level is the reference level



Quiz: What is matrix formulation of the linear model?




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, Ans: Y = XB + e



- Y is the response vector

- X is the design matrix

- B is the vector of p+1 (including intercept) regression parameters

- e is the vector of error terms



Ex: Y = [Y1, Y2....]

B = [B0, B1, ...]

E = [e1, e2,...]



Quiz: F-test hypotheses

Ans: Ho: response is not related to any of the predictors



Ha: response y is related to at least one of the predictors in the model



Quiz: Bias-Variance tradeoff




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, Ans: As complexity in model increases (more predictors), bias decreases but
variance increases



- We want to control both bias and variance



Quiz: Bias

Ans: Bias(μˆ) = E[μˆ] − μ



Bias arises because of the model misspecification (banana shape but fit a linear
regression) WRONG MODEL



Quiz: Variance

Ans: Var(μˆ) = SE(μˆ)^2



Arises due to noise in estimating regression coefficients



Quiz: Mean squared error (MSE)




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