7.2 Goodness of Fit and Hypothesis Test Flashcards
What is the coefficient of determination?
The percentage of the total variation in the dependent variable explained by the independent variable
For simple linear regression with one independent variable, how do you compute the coefficient determination?
It is the square of the correlation coefficient
What is the calculation for the coefficient of determination that can be used on linear regressions with either a single or multiple independent variables?
R² = RSS / SST
What is SST?
SST = Total Sum of Squares
It measures the total variation in the dependent variable
It is equal to the sum of the squared differences between the actual and the mean value of Y
What is RSS?
RSS = Regression sum of squares
It measures the variation in the dependent variable that is explained by the independent variable
It is the sum of squared distances between the predicted Y-values and the mean of Y
What is SSE?
SSE = Sum of Squared Errors
SSE measures the unexplained variation in the dependent variable
SSE is the sum of the squared vertical distances between the actual Y-values and the predicted Y-values
What equals SST?
RSS + SSE = SST
What is MSR? (Mean Square of Regression)
MSR = The explained variation divided by K
RSS / k
Where explained variation = RSS and K = degrees of freedom
At Level 1, K will always = 1… so MSR = RSS/1 = RSS
What is MSE? (Mean Square of Error)
MSE = SSE / (n-k-1)
It is a variance computation… we are looking at the variance of the error terms
The variance of the actual values against their forecasted values
What is the SEE? (Standard Error of Estimate)
The SEE = Square root of MSE
It is the standard deviation of the errors
The lower the SEE, the better the model fit
What does a high and a low R² value indicate?
High R² = low SEE (good fit)
Low R² = high SEE (poor fit)
What does the F-stat assess?
What is it known as?
How many tails?
How well a set of independent variables (as a group) explain the variation in the dependent variable
A test of overall model significance
It is ALWAYS a one-tailed test (right hand tail)
What is the F-test null and alternative hypothesis?
Null: Slope coefficient = to 0
Alternative: Slope coefficient not equal to zero
What are the F-test degrees of freedom?
There are two degrees of freedom
Numerator = K
Denominator = N-K-1
How do you use a t-test to test explanatory power?
In multi-linear regression, the F-test is used to determine whether any of the independent variables have explanatory power. If the answer is yes, a t-test is used to determine which individual independent value(s) has/have explanatory power
How do you calculate the F-stat?
