Basic of multiple regression

the difference between Simple and multiple regression

simple regression compares if line fits data, multiple regression compares if multiple variance is worth the trouble compared to simple regression

Assumption of Multiple Regression: the relationship between dependent variable and independent variable is

liner

Assumption of Multiple Regression:is the independent variable random?

no

Assumption of Multiple Regression: relationship between two or more independent variable

there is no define liner relationship between them

Assumption of Multiple Regression: Expected value of the error term equals to

0

autocorrelation

when a time series model next value is determine by the previous value. Model accuracy is reduced, estimated standard error is overrated

which test tests for auto correlation

durbin watson (DW)

multicollinarity

2 or more independent variables are highly correlated , high standard error low t test

Heteroskedasticity

variance of the error term is not constant

Logistic regression predicts

true or false; and fits a S shape progression ; can use continues data like (size, length) and also descrete date like true false

The normal Q-Q plot is useful for

exploring whether the residuals are normally distributed

A pairwise scatterplot is used to detect whether

there is a linear relationship between the dependent and independent variables

AIC and BIC, lower better or higher

lower

AIC and BIC is each used for

AIC is used if the goal is to have a better forecast. BIC is used if the goal is a better goodness of fit.

what does it mean if adjusted R2 is lower

meaning adding the last variable does not make the model better

difference in T test and F test

T test compares mean of two group to see if they are different, F test compares Variance of two group to see if they are different . ie check if two stock price is different (t test) vs if the volatility of two stock is different

can R2 detect the statistical difference of coefficient

no

a poor model can have high R2 because of

overfitting

adjusted R2 penalizes extra

factor added to the model

R2 increase when t test

>\1\

f test if all independent variable explain dependent variable

reject the null if F value

> critical value

what does rejecting null mean

at least one of the variable is doing a good job

p value is

how confident you are at you at you model

p value ranges from —- lower better or higher better

0-1 , lower the better

a p value of 0.05 which is commonly used threshold means

if we run a bunch of experiment, 5% at a time it is wrong (false positive)

can adjusted r2 be negative or decline

When a new independent variable is added, adjusted R² can decrease if adding that variable results in only a small increase in R². In fact, adjusted R² can be negative, although R² is always nonnegative. Adjusted R² can be negative as well as decline.

AIC or BIC which one penalizes for over fitting (too many independent variable)

BIC