Unit 7 Flashcards
What is the Model I of the general linear model?
theoretical and simplified approximation of reality that allows it to be explained, controlled and predicted
What is the General Linear Model?
Set of parametric analyses that aim to predict a variable based on one or more variables, assuming that the relationship between them is linear
What are common foundations for many statistical methods?
Correlation
Student’s t
ANOVA
Linear regression
What is the formula of linear function?
𝑌’ = β 0 + β 1 · X i
What is the general linear model based on?
the least squares method:
Deviation -> Residues
-> 𝜀= Y - Y’
What is the closes analysis of the general linear model?
linear regression
What does linear relationship (r) evaluate?
Does one variable change as a function of another?
What does Linear regression evaluate?
how much does one variable change as a function of another?
What is required for the linear regression?
at least two quantitative variables that are linearly associated
- Simple regression model: One predictor
- Multiple regression model: More than one predictor
Is the linear regression model a mathematical one?
no, it is a statistical model
What is the difference between a mathematical and a statistical model?
a statistical model includes terms that represent the error/residue that we can make when
making a prediction of Y
When are the predictions the most accurate?
when the error is the smallest
What is the equation of the linear regression model?
𝑌’ = β 0 + β 1 · X i + 𝜀
Where is error NOT included and why?
in a sample linear regression model
- We are fitting a line (in linear regression, a straight line) between the data from the Independente Variable (IV) and the Dependent Variable (DV), based on the means of the X and Y values (of observed, estimated scores, and residuals), not on the specific errors of each observation or data.
- Residuals are the error of the model and are considered an outcome. They are evaluated after the model is fitted to see if it predicts well
What does Y’ stand for in the equation of the regression line?
Predicted value, Outcome variable (dependent)
What does x stand for in the equation of the regression line?
Observed value, Predictor (independent) variable
What does b0 stand for in the equation of the regression line?
constant at origin (also called 𝑎) = intercept = value of Y when X is zero = Value of Y not affected by X
What does b1 stand for in the equation of the regression line?
slope = regression coefficient = hoe much Y changes by one unit
What does Ɛ stand for in the equation of the regression line?
residual (difference between the observed and predicted value) (Y - Y’)
How do we calculate the slope?
formula based on covariance: b1 = Sxy : S²x
How do we calculate the intercept?
b0 = Y’ - b1 x X’
Why can part of the variability of Y be explained by the variability of X?
because the two variables are related linearly
what proportion of the Dependent Variable (Y) can be explained by the
Independent Variable (X)?
R2 = Coefficient of determination = r xy 2
What is R² used to?
to know the predictive capacity of X (or predictors ) on Y.
What does ANOVA (Snedecor’s F) indicate?
if the model provides a good degree of prediction of the result variable.
- Goodness of fit: how good does the estimation fit the data
- Null hypothesis: It doesn’t have a good adjustment
- Alternative Hypothesis: It has a good adjustment.
What does the regression model predict?
the behavior of the variable Y from a variable X (X 1)
What does the multiple regression model predict?
prediction of the variable Y (DV) by two or more variables X
(independent or predictor variables ) ( X 1 , X 2 , X 3 …)
What are the requirements of the Parametric Regression Model?
a) Homoscedasticity: equality of variances.
b) Normal distribution of the residuals .
c) Independence of the errors (the residuals are not related).
d) Absence of multicollinearity: absence of relationship between the predictors (VI) [Only check in multiple regression]
