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Statistics 2 8
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- 1Adding more predictors means...> we still only predict a single model, but the number of predictors of
this model has increased
--> leads to an improvement of the model ---> correlation between the model and the dependent variable (R) went up - 2Standard error of the estimate isroot mse
- 3if the model as a whole is significant...there will be at least one significant predictor
- 4If the model in its entirety is not significant...it’s pretty safe to assume the predictors are not significant either.
- 5standard deviation reflects...how far the individual scores are from the line of predicted scores
- 6standard deviation representsunexplained variance
- 7r squared equalsssm/sst
- 8What will happen to R² when we add a predictor that is completely unrelated to the dependent variable?As no additional variance will be explained in the dependent variable, R² will not change.
- 9What will happen to R² when we add a predictor that is completely unrelated to all other independent variables, and negatively related to the dependent variable?As additional variance will be explained in the dependent variable, R² will increase
- 10Modelshows the predictors in the model, including b0, here always called “(Constant)”. In this
case, there are three predictors: “X1”, “X2”, and “X3 - 11B:> Because the model now has more variables, the interpretation of the b-coefficients has also
changed:
b0: Value of y when all predictors are 0
bp: If the corresponding predictor changes by 1, then y changes by bp, given that all other predictors
remain constant - 12Std. Error:> This shows the standard error of the regression coefficients
> represents the uncertainty in the
corresponding B-coefficients when trying to generalize them to the population. ---> they are
the standard deviation that we will find for these specific coefficients, if we were to repeat this experiment multiple times.
> What is most important to remember is that these values do not reflect
the spread of the individual scores, but only the hypothetical spread of the coefficients of the model - 13Beta:> shows the standardized regression coefficients.
> The ß is no longer equal to the correlation between any given predictor and Y. As this is standardized,
this is a more “fair” way to compare which variable is better at predicting the dependent variable
than the unstandardized regression coefficients, because the unstandardized coefficients are
influenced by their standard deviation. Although later, in lecture 9, we will find even better
coefficients to determine which variable contributes the most. - 14When 0 (value of null hypothesis) is included in this confidence intervalthe coefficient is not statistically significant.
When 0 is not included in this confidence interval, the coefficient is statistically significant - 15Is R positive or negative when all predictors have a negative slope?R will always be positive. Remember that the model is represented by the line that is going straight through the points, regardless of how the points are distributed. If the points (observed values) increase, the line (predicted values) increases with them.
A negative relationship will lead to, as we can see, a negative slope. The actual correlation between
the independent variable and dependent variable is e.g. -0.568, but the correlation between the model
(line) and the dependent variable (height of observations) is positive, specifically e.g. 0.568. - 16—
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- Descripción
- Psychologie Fichas sobre Statistics 2 8, creado por Adrian Mayer el 08/01/2019.
- Creado por
- Adrian Mayer · ene 2019
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- 9 ene 2019
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