Topic 7: Empirical Issues Flashcards
How would you find the SST for a model with SSR given?
R^2 = 1- SSR/SST
The change in y caused by a change in x in a model with a quadratic x is?
The partial derivative of the model WRT x.
When another variable is added to a model, the R squared only goes up or down?
It only can go up. However, the adjusted R squared can go up or down.
What is adjusted R Squared?
A goodness of fit measure in MLR analysis that penalizes additional explanatory variables by using a degrees of freedom adjustment in estimating the error variance.
What is over-controlling?
Including explanatory variables that should not be held fixed when studying the ceteris paribus effect of one or more other explanatory variables, like when an explanatory variable is a pathway through which the variable of interest affects the dependent variable.
What is a prediction interval?
A confidence interval for an unknown outcome (prediction, fitted estimate) on a dependent variable in a MLR model. Is always wider than CI.
What is the predicted effect from a one unit increase in x1, holding x2 constant in a model with a quadratic (and multiple x1 terms and holding other terms constant)?
It is the partial derivative of the model with respect to x1.
How would you find an estimated increase in y given beta1x2 + beta2x2, where x2=50?
You would run a regression, find the estimated coefficients for beta1 and beta2. Plug all numbers into the equation (including 50) to get the change in y.
How does data scaling affect the independent and dependent variables?
Changing the scaling of the y variable changes every else the same about, but changing the x variable, only changes that one. If your x is now divided by 100 your beta coefficient for that will be the inverse, times 100 to make the y value and all others the same.
What are beta coefficients?
Also known as standardized coefficients, you calculate the z score by subtracting the mean from the estimate and dividing by standard error, we know know how many “standard units” (deviations) that value is.
What is useful about standardized coefficients?
If they are all standardized in a regression, you can tell which is the most important by which is the biggest.
What is the maximum value of a quadratic function?
x* = | (beta^1) \ (2beta^2) |
