01 Intro

Question 1

Regression Analysis

Answer 1

investigates quantitative, predictive relationships

Question 2

Response Variable (Y)

Answer 2

dependent variable which serves as a response, quantity we are trying to predict
(X1,Y1),(X2,Y2),…,(Xn,Yn)

Question 3

Predictor Variable (X)

Answer 3

independent variable which serves as a predictor, often known as a covariate or feature
(X1,Y1),(X2,Y2),…,(Xn,Yn)

Question 4

Conditional Expectation in Regression

Answer 4

E(Y|X = x),

Question 5

Regression Function

Answer 5

x|->E[Y|X = x]
Ex) how the mean response differs across possible values of Covariate X

Question 6

Expanded Regression Function and Conditional Expectation Form

Answer 6

x = (x1,x2,…xp) |-> E[Y|X = x] = B0 + B1x1 + B2x2 + … + Bpxp

Question 7

Regression Parameters

Answer 7

the p + 1 coefficient (one for each covariate and the additional one, B0, for the intercept)
x |-> E[Y|X = x]
= a + Bx

Question 8

Linear Model to Estimate Regression Parameters

Answer 8

x = (x1,…,xp) |-> u(hat) (x) = B(hat)0 + B(hat)1x1 + B(hat)2x2 +…+ B(hat)pxp

Question 9

Prediction

Answer 9

quantify how well linear regression model “fit” the data in the sense of being able to predict an unforseen data point (Xnew, Ynew)

Question 10

Predictive Mean Squared Error

Answer 10

E[(Ynew -u(hat)Xnew)^2]

Question 11

Inference

Answer 11

assess how accurate the estimators of regression coefficients are

Question 12

Observational vs Experimental Data

Answer 12

randomized experiment - manipulate the value of the predictor value to isolate its effect on the response variable

observational study - researcher still care about the effect the predictor has on the outcome but they are more likely to just observe the nature of the relationship between predictor and response as they occur

Question 13

Confounder variables

Answer 13

Ex) people who take multivitamins have fewer heart attacks. but - if people who take multivitamins smoke less and exercise more than people who don’t take multivitamins.
association between multivitamins and heart attack is confounded by exercise and smoking

Question 14

Regression Analysis in Observational Studies

Answer 14

regression analysis allows for statistically sounds conclusions about the association between the response and covariate - NOT causation

Question 15

The Capital-Asset Pricing Model (CAPM)

Answer 15

univariate regression model that relates to the excess return of an asset to the excess return of the market

Formula 1:
Rt = (P(t) - P(t-1))/(P(t-1))

Formula 2:
R(t) - v(t) = a +B (M(t) - v(t)) + E(t)