Unit 7

Question 1

What is the Model I of the general linear model?

Answer 1

theoretical and simplified approximation of reality that allows it to be explained, controlled and predicted

Question 2

What is the General Linear Model?

Answer 2

Set of parametric analyses that aim to predict a variable based on one or more variables, assuming that the relationship between them is linear

Question 3

What are common foundations for many statistical methods?

Answer 3

Correlation
Student’s t
ANOVA
Linear regression

Question 4

What is the formula of linear function?

Answer 4

𝑌’ = β 0 + β 1 · X i

Question 5

What is the general linear model based on?

Answer 5

the least squares method:
Deviation -> Residues
-> 𝜀= Y - Y’

Question 6

What is the closes analysis of the general linear model?

Answer 6

linear regression

Question 7

What does linear relationship (r) evaluate?

Answer 7

Does one variable change as a function of another?

Question 8

What does Linear regression evaluate?

Answer 8

how much does one variable change as a function of another?

Question 9

What is required for the linear regression?

Answer 9

at least two quantitative variables that are linearly associated

• Simple regression model: One predictor
• Multiple regression model: More than one predictor

Question 10

Is the linear regression model a mathematical one?

Answer 10

no, it is a statistical model

Question 11

What is the difference between a mathematical and a statistical model?

Answer 11

a statistical model includes terms that represent the error/residue that we can make when
making a prediction of Y

Question 12

When are the predictions the most accurate?

Answer 12

when the error is the smallest

Question 13

What is the equation of the linear regression model?

Answer 13

𝑌’ = β 0 + β 1 · X i + 𝜀

Question 14

Where is error NOT included and why?

Answer 14

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

Question 15

What does Y’ stand for in the equation of the regression line?

Answer 15

Predicted value, Outcome variable (dependent)

Question 16

What does x stand for in the equation of the regression line?

Answer 16

Observed value, Predictor (independent) variable

Question 17

What does b0 stand for in the equation of the regression line?

Answer 17

constant at origin (also called 𝑎) = intercept = value of Y when X is zero = Value of Y not affected by X

Question 18

What does b1 stand for in the equation of the regression line?

Answer 18

slope = regression coefficient = hoe much Y changes by one unit

Question 19

What does Ɛ stand for in the equation of the regression line?

Answer 19

residual (difference between the observed and predicted value) (Y - Y’)

Question 20

How do we calculate the slope?

Answer 20

formula based on covariance: b1 = Sxy : S²x

Question 21

How do we calculate the intercept?

Answer 21

b0 = Y’ - b1 x X’

Question 22

Why can part of the variability of Y be explained by the variability of X?

Answer 22

because the two variables are related linearly

Question 23

what proportion of the Dependent Variable (Y) can be explained by the
Independent Variable (X)?

Answer 23

R2 = Coefficient of determination = r xy 2

Question 24

What is R² used to?

Answer 24

to know the predictive capacity of X (or predictors ) on Y.

Question 25

What does ANOVA (Snedecor’s F) indicate?

Answer 25

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.

Question 26

What does the regression model predict?

Answer 26

the behavior of the variable Y from a variable X (X 1)

Question 27

What does the multiple regression model predict?

Answer 27

prediction of the variable Y (DV) by two or more variables X
(independent or predictor variables ) ( X 1 , X 2 , X 3 …)

Question 28

What are the requirements of the Parametric Regression Model?

Answer 28

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]