Chapter 7 - Intro to Linear Regression

Question 1

Simple Linear Regression

Answer 1

Explain the variation in a dependent variable in terms of the variation of a single independent variable

Question 2

Variation in Y (linear regression)

Answer 2

sum of all (Yi - Ybar)^2 . Meaning, Variation in Y = the sum of all (variable Y - Avg Y)^2

Question 3

Dependent variable

Answer 3

Y. Variation is explained by independent or X. Also known as explained, endogenous, predicted.

Question 4

Independent Variable

Answer 4

Variable that explains the variation of Y, or dependent variable. Explanatory, exogenous, predicting.

Question 5

Linear Regression Model: Yi=b0+b1Xi+Ei, i=1,…, n

Answer 5

Yi = ith observation of the dependent variable, Y. Xi = ith observation of the independent variable, X, b0 regression intercept, b1 = regression slope coefficient, ei = residual for the ith observation (disturbance or error)

Question 6

b0

Answer 6

regression intercept term

Question 7

b1

Answer 7

regression slope term

Question 8

Ei

Answer 8

residual for the ith observation (disturbance / error).

Question 9

^Y i = ^b0 +^b1Xi, i=1,2,3,..n

Answer 9

Linear Equation/Regression line

Question 10

Regression line: ^Yi, ^b0, ^b1

Answer 10

Estimated value of Yi given Xi, estimated intercept term, estimated slope term.

Question 11

Sum of Squared Errors SSE

Answer 11

Sum of squared vertical distances between actual Y values and predicted Y values regression line minimizes this

Question 12

^b1

Answer 12

Slope coefficient; Change in Y for unit 1-change in X. COVofXY/σ^2ofx

Question 13

^b0

Answer 13

=y ̅-^b1x ̅. Intercept - estimate of dependent variable, when independent (X) variable is zero.

Question 14

Linear Regression Assumptions

Answer 14

1. A linear relationship exists between the dependent and independent variables. 2. The variance of the residual term (e/error) is constant for all observations (homoskedasticity). 3. The residual term is independently distributed; that is, the residual for one observation is not correlated with that of another observation. 4. The residual term is normally distributed.

Question 15

Homoskedasticity

Answer 15

Prediction errors all have same variance.

Question 16

Heteroskedasticity

Answer 16

Assumption of homoskedasticity is violated.

Question 17

ANOVA analysis of variance

Answer 17

analyzes the total variability of the dependent variable

Question 18

Total sum of squares SST

Answer 18

∑_(i=1)^n (yi-y ̅ )^2 . Measures the total variation in the dependent variable. Equal to the sum of squared differences between actual Y value and mean of Y.

Question 19

Sum of squares regression (SSR)

Answer 19

Measures variation in dependent variable explained by INDEPENDENT variable. Sum of squared differences between PREDICTED Y and mean of Y. Sum of (^Yi -y ̅ )^2.

Question 20

Sum of squared errors (SSE)

Answer 20

Measures unexplained variation in dependent variable. SSE = SST- SSR. Sum of squared vertical distances between actual Y and PREDICTED Y. sum of (Yi-^Y)^2.

Question 21

MSR (Mean sum of square, SSR)

Answer 21

SSR/1 = SSR. MSR is SSR.

Question 22

MSE (Mean sum of square, SSE)

Answer 22

SSE/n-2.

Question 23

SEE

Answer 23

square root of MSE. Standard deviation of residuals. Lower SEE, better model fit.

Question 24

R^2

Answer 24

Coefficient of determination. % of total variation in dependent variable explained by independent variable. R^2 = SSR/SST.

Question 25

F test

Answer 25

MSR/MSE. One tailed test. How well a set of independent variables, explain variation in dependent variable. Reject H0 if F>Fc.

Question 26

Predicted Value ^Y

Answer 26

^Y = ^b0 +^b1Xp

Question 27

Log - lin model

Answer 27

Dependent variable is log while independent is linear

Question 28

Lin- log model

Answer 28

Dependent variable is linear while independent is logarithmic. Absolute change in dependent for relative change in independent.

Question 29

Log-log

Answer 29

Dependent variable and independent variable are log. Relative change in both.