Simple and Multiple Linear Regression- Austin

focus on 3 confounding effects

What is the definition of homoscedasticity?

What is the definition of homoscedasticity?

• Variance- vertical shape

  • AKA how “flat” the data is

How does an investigator deal with bias?

variable control

In observational studies it is hard to account for _______, but we can still do what?

In observational studies it is hard to account for bias, but we can still identify and account for them.

What is the definition of bias?

anything that can non-randomly skew my results

Statistical methods used to account for sources of bias are called ________________________.

regression analysis

What is a confounder?

any factor that prevents appropriate statistical interpretation of results within practical context of a study

What is an omitted variable?

a specific and observable factor that is omitted from the analysis

T/F: All omitted variables are confounders, but not all confounders are omitted variables.

T

What does the magnitude of bias refer to?

difference between the average confounded sample estimate and the non-confounded population parameter.

If I did a regression analysis not accounting for bias, then I did a regression analysis including the bias, the results of the FIRST regression analysis would be considered _______________.

inefficient

What are 3 types of confounders?

• mediating effect

• modifying effect

• confounding effect

What is the mediating effect?

a mediator is an intermediate between the independent and dependent variable

What is the modifying effect?

alters the degree (strength) and/or direction of the relationship between the independent and dependent variable

What is this equation used for? What does each of the variables mean?

This is the equation for linear regression.

Y_i= dependent variable

b₀= intercept

b₁= slope coefficient

X_i= independent variable

u_i= error term

Will “u” or the error term be the same for each data point?

no

The error term is also referred to as the ________________.

residual

The sum of all residuals is equal to ___.

0

Simplest regression analysis is ___________________________________(____).

Ordinary Least Squares (OLS)

For OLS the dependent variable must be _____________________. (continuous or discrete)

continuous

What are the assumptions for OLS?

• random sampling

• normal distribution

In analyzing OLS, what is the null and alternative hypothesis? What do each of these mean in terms of a linear relationship?

null= no linear relationship

alternative= there is a linear relationship

What parameter assess how well the trend line fits the data?

R²

An R² of 0.8 would indicate what?

the line fits the data pretty well

Unlike linear regression, multiple regression accounts for _______.

bias

What is this equation used for? What does Z and ε stand for?

This equation is used for multiple regression.

Z stands for the confounder

ε is the error term/residual

Will ε be larger or smaller than u? Why?

ε will be smaller

• why? less bias, less error in multiple regression

What is the ONE EXCEPTION to when ε is NOT smaller than u?

If there are superfluous regressors ε=u

What is a superfluous regressor?

variable that doesn’t mean shit

• example: how many clouds were in the sky on the day you measured the patient’s weight

By looking at _____ values for multiple and linear regression you can see the magnitude of bias/ how much bias omitting that variable caused.

b₁

What is the marginal effect?

How is y effected by a small change in x

In multiple regression can we use R²? Why or Why not?

NO must use adjusted R²

• this is because R² can be effected by superfluous regressors

When is a dummy variable used?

used to include discrete(dichotomous) variables in our regression analysis

Dummy variables use the ______ coding scheme and can ONLY be _____ or ______.

Dummy variables use the a-1 coding scheme and can ONLY be 0 or 1.

Dummy variables cannot represent what?

marginal effect

In unstandardized multiple regression we cannot do what? What is the solution to this problem?

we cannot say which variable had the most impact because there are a bunch of different units (ex: you can’t compare age in years to height)

• solution: standardization of units (turn variables in to z-score)

Standardized mutliple regression is ONLY for ________________, not marginal effect.

comparing variables