Test 3 - Social Statistics II

F-stat is always ____

positive

The ____ your f-stat the ____ we will reject the null hypothesis

larger, more likely

P-value

If the null is true, than the likelihood we get a statistic less than the p-value (i.e., 0.05) is less than 5%.

What is testing overall significance?

It helps us by adding all the predictors of the model. It will help accurately predict the y-value.

Omnibus test

All predictors in the model are tested

Dummy variables

• Incorporate qualitative explanatory variables into a linear model

• One variables has two possible values, 0 or 1

• Goes by many names such as indicator, dichotomous, qualitative, etc

• Arbitrarily assign value 1 to one category and 0 to the other

Why do we include dummy variables?

• We want to understand the variation in DV

• To avoid biases in X and Y

Polytomous variable

Categorical variable that can take on more than two distinct categories or levels (i.e., political parties).

Gamma (γ)

Tells us the difference between our independent variables.

In a polytomous graph, all the dummy variables need to add up to ___

one

What does it mean for the b1 of B1 to be unbiased?

It means if we draw numerous samples from the population on average, the slope co-efficient will be the same as the population parameters. 

In what circumstances is R^2 equal to 1

When all the predictors explain all the outcomes in y the R^2 is equal to 1.

How do we compare the impact of different variables

We look at the Beta coefficient (last column in Stata). The larger the number the greater impact it will have on the y variable.

How do you interpret RMSE?

On average, when we use the regression to tell us how the observed y and the expected y differ. (i.e., tells us how many hours worked and the actual hours worked. The difference is 14.136).

How to interpret the beta co-efficient?

For every one unit change in x, we see a one unit change in y, holding all other variables constant.

How do we tell which model is a better fit?

• Look at the adjusted R-squared. Whichever one is bigger is the better model.

• Smaller RMSE (because it shows the difference between observed and predicted y)

Confidence interval

It tells us that we are alpha (maybe 90, 95, or 99%) sure our data lies within the confidence interval. 

What is the formula for categorical dummy variables?

• m - 1

• m = number of categorical variables

What does b1 and b2 mean (multivariate regression)?

Difference in the y variable between explanatory variable (i.e., difference in the number of kids [y] between democrats [b1] and others [b2]).

In a dummy variable equation, what does the constant mean?

• All the variable predictors at 0

• I.e., When slope is 0 the person is other (not democratic or republican) and when gender is 0 the person is male

How do we look at the difference between two dummy variables in Stata?

We omit one variable when we want to understand the difference between two variables (i.e., we omit republicans [or democrats] when we want to understand the difference between both parties).

Adjusted R²

• Use to compare models with different predictors

• Model with a higher adjusted R is generally considered a better fit

• It will increase only if a new variable improves the model more than would be expected by chance

Restricted model

• Less complicated model, more simple

• Restricting the relationship between effort (variables will be set to 0)

Unrestricted model

• More complicated model, more fuller

• It has more variables

What does the constant (alpha) mean?

• All the variable predictors at 0

• (i.e., When slope is 0 the person is other, which means they are not democratic or republican)

When do we use f-test

• When we have different variables under the same umbrella (i.e., education —> less than high school, high school, college, etc)

• Compare restricted and unrestricted models

What does the mean tell us for categorical variables?

• Show us the proportion of respondents that fall under the category

• I.e., mean = 0.75 for females (this means that 75% of respondents are females)

Models with interactions are _____ not additive

multiplicative

Interactions

Describes a situation where the effect of one predictor variable on an outcome variable depends on the level or value of a second predictor variable.

A model with an interaction suggests:

\text{Effect of A and B} \neq (\text{Effect of A}) + (\text{Effect of B})

Equation for an interaction

\hat{Y} = b_0 + b_1X_1 + b_2X_2 + b_3(X_1X_2)

Interaction co-efficient b₃

Tells you about the interaction effect. If b₃ is statistically significant, an interaction is present.

B1 (Coefficient for X1)

• The expected change in Y for a one-unit change in X1 ONLY when X2 is equal to zero.

• (i.e., The number of children for women when sibship is zero)

B2 (Co-efficient for X2)

The expected change in Y for a one-unit change in X2, ONLY when X1 is equal to zero.