ECON 391 UKY Exam 2

SST Formula

SST Formula

SSE + SSR = SST

What is SSR

sum of squares regression (THAT IS EXPLAINED by the model)

What is SSE

sum of squared errors (THAT IS NOT EXPLAINED by the model)

R squared

coefficient of determination

R squared formula

SSR/SST

standard error formula

standard deviation/ square root of n

Margin of Error Formula

confidence level * Standard Error

dummy variable

A variable used to convey qualitative information in a regression model

The regression sum of squares (SSR)

The explained part of the variation in the dependent variable

Explained Variation formula

total variation - unexplained variation

r squared formula

(total variation - Unexplained Variation) / Total Variation

r squared (coefficient of determination)

The percentage of variation in the dependent variable that is explained by the independent variable

what does margin of error account for

Error due to random chance only nothing specific

standard error

the variability of the predicted y-values around the observed y-values

What can happen to R squared when adding a variable

adding a variable cannot decrease the R squared

What happens when r squared = 1

SSR = SST

only valid dummy variables

0 and 1

The coefficent of a variable after we run a regression

our estimation for the average impact of that independent variable on the dependent variable, all other variables held constant

SSE can never be

larger than SST (SSE is a part of SST)

Rsquared equation

[ (SST - SSE) / (SST) ] aka (SSR/SST)

The error term

the part of regression equation that accounts for all variables not included in the model

What is true about a multiple regression analysis

you can only have one dependent variable

The Y intercept

The value of Y when all the X's are Zero

The residual

the difference between an observed value and estimated value

Why do we square the error?

positive and negative errors could cancel each other out

SSR formula

Summation (((Y^ - Y(bar))^2)

What do we do with adjusted R squared?

We make determinations between models using adjusted R squared (pick the model with higher adjusted R squared)

What do we do with the sample size if we want to cut our margin or error to 1/3 of what it is?

Get a sample size 9 times as large

What do we do with a confidence interval

We get a range of values for what we believe we can find the population means for a given confidence level

Standard formula for a confidence interval

(point estimate) + and - Margin of error

What happens to margin of error when the level of confidence decreases?

The MOE becomes smaller (Za/2) (shrinks in the formula)

Multiple regression equation

The mathematical equation that explains how the dependent variable Y is related to several independent variables X1, X2 and the error term ε

In the model Y = β0 + β1 X + β2 D + β3 X*D + ε, the interaction variable causes

(The interaction variable is D)

a change in just slope

How is adjusted R squared different from regular R squared?

Unlike the regular 𝑅2, the adjusted-𝑅2 will decrease if the additional independent variable doesn't increase the amount of variation in the dependent variable

(ONLY ADJUSTED 𝑅2 can decrease if more variables are added)

standard deviation

is variance squared

When deciding between two models with a different number of independent variables

pick the one with the higher R squared

What happens when you increase the sample size?

- Decrease the standard of error (SE) or variability
- Increase the precision around the true mean

What is the possibility when you increase the same size

You increase the likelihood that a sample mean will fall within some given distance of the true mean

What is the advantage of minimizing the sum of the squared errors rather than just the sum of the errors?

Larger errors are given more weight than smaller ones

(squaring the errors puts a larger relative weight on the larger errors instead of averaging the absolute value of errors)

What is margin of error?

Variation in the random sample due to chance