Flashcards
stats 3 lecture 1+2
Cards in this deck (30)
- 1Ordinary Least Squares (OLS)we choose a model with the smallest sum of residuals
- 2NormalityThe pp-plot plots the expected normal distribution against the observed distribution. Ideally, the
points would follow the reference line, meaning that the expected and observed distribution are
identical, and therefore exactly normal. - 3HomoscedasticityThe residual plot plots the predicted values against the residuals, so we can check whether the
(vertical) spread of the residuals is equal for any predicted value. - 4linearity- residual plot works but
- creating a partial regression plot for every separate predictor is better - 5slopesreally called Partial unstandardized regression coefficients, indicating that the overlap with
other predictors is removed. We represent this in the interpretation by “keeping the other predictors
fixed”. - 6when a predictors has higher degrees of multicollinearity- interpretation problems for individual predictors
- increases
the standard error of the slope of that predictor ( more uncertainty and a lower
likelihood to reject the null hypothesis.)
- check the degree of multicollinearity with VIF, which
is generally fine when it is 4 or lower. - 7how to identify outliers- DFFIT, DFBETA or Cook’s distance for every observation
- standardized version of DFBETA and Cook’s distance indicate problems when we find values higher
than 1. - 8Semi-partial correlationThe correlation between the unique part of a given
predictor, that does not overlap with other predictors,
and the dependent variable as a whole - 9Partial correlationThe correlation between the unique part of a given
predictor, that does not overlap with other predictors,
and the part of the dependent variable that does not
overlap with other predictors - 10R- Multiple Correlation
- 11R^2adj. (R^2 w)Adjusted explained variance
- Proportion of the variance of the dependent variable that can be explained by the model as a whole, adjusted for the inflation in R² simply caused by adding predictors to the model - 12F-valueThe test value that reflects how much variance in the dependent variable is explained by the model
- 13For one predictor, how to find out standerdized slopeit is r (just that)
- 14Value of the intercept when the slope is standerdized- Has no value
- Standardization means transforming a distribution of scores to
have a mean of 0 and standard deviation of 1. When all variables are standardized, the mean is 0 for
all variables, turning the formula for intercept into: 0-0-0-0=0 - 15t-value (plus formula and DF)- test value of choice for the coefficients table, as the t-distribution excels in
conditions when the standard deviation of the population is not known
- - 16how to use the tableNote that when looking up a t-value in the table, the p-values in the top row are one-sided. If you
need the two-sided p-value, which you often do, do not forget to multiply the p-value by 2. - 17- H0: b = 0 the p-value we find because of this null hypothesis is exactly equal to the p-value we would find if we test any of the following:- H0: b* = 0
- H0: sr = 0
- H0: pr = 0 - 18calculate the confidence interval of any regression coefficient bb ± t ∗ SEb
, df = DFEe = n − p − 1 - 19Interpretation of a CIIf we were to create this
particular confidence interval for many different samples from the same population, XX% of them
would include the true population slope of b - 20Looking for the value in a 95% confidence interval corresponds to...a two-sided significance test with alpha = 0.05. When the value of 0 is included in the 95%
confidence interval, this corresponds to not rejecting the null hypothesis at alpha = 0.05. When 0 is not
included, we would reject the null hypothesis. - 21VIF (plus formula)- show the level of multicollinearity
- A VIF of 1 means that there is no multicollinearity, while a VIF of 4 of higher indicates a problem - 22VIF increases exponentially , meaning...- the difference between 1.0 and 1.1 needs more change in R^2j
than 3.9 to 4.0. However, when the highest VIF is less than 2, multicollinearity is
definitely not a problem. - 23with 1 predictor, the semipartial correlation is- r
- (semipartian variance is r^2) - 24sr (sr^2) for 3 predictors= R^2 of the full model − R
2 of model without predictor i
(we can see that the semi-partial explained variance is
identical to the change in R² when the predictor is added to the model.) - 25The standard error of the estimate isthe square root of the Mean Square
Residual. - 26effect sizes of R^2 (when low medium high?)Small: R^2 = 0.01
Medium: R² = 0.06
Large: R² = 0.15 - 27relationship R², n, and p for adjusted R².If R² & n are higher, adjusted R² is higher. If p is higher, then adjusted R² decreases – potentially to a negative number.
- 28Partial correlation- Correlation between Y and X1 where
X2 is partialled out of both (held
constant)
- Which PROPORTION of the variance of Y not explained by the other IVs, is uniquely explained by this IV? - 29semi partial correlation- Correlation between Y and X1, where X2 is removed from X1 only
- Answers the question: How much TOTAL variance of Y is uniquely
explained by this IV? - 30Why adjusted r^2?r^2 overestimates p^2
(population squared multiple correlation).
r^2 must be adjusted, or shrunken.
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- Flashcards on stats 3 lecture 1+2, created by Adrian Mayer on 25/02/2020.
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