Pseudoreplication- Anwerstreating many measurements from same individuals as if
independent.
assessing the biasing effect of an error & error modelling can only be done if...- Anwersif the
error structure (model) & respective parameters are known. thus, potential errors must be
identified already in the planning phase
what is a model?- Anwersapproximation of reality. helping to understand the real world through
simplified assumptions
interpretation of linear dependency- Anwersthere's a proportional increase in y (response
variable) with increase/decrease of x (explanatory variable)
What does the error term ei take into account?- Anwersthe fact that the linear relationship
doesn0t describe the data perfectly
Degrees of freedom in linear regression- Anwersn–2
What's R^2 ?- Anwersin simple linear regression, it's the correlation btw the independent & the
dependent variable.
indicated the proportion of variability of the response variable y that's explained by the
ensemble of all covariates.
value between 0 and 1
the larger R^2, the more variability is explained by covariate, the better the choice of covariates
(doesn't say anything about Model quality)
,T–test
Df=- Anwershypothesis test that allows to compare means
one–sample t–test
two–sample t–test
Df: n–2
one–sample t–test- Anwerstests if the mean of a sample differs from some value
two–sample t–test- Anwerstests if there is a difference between the mean of one sample and
the mean of another
p–value =- Anwersprobability of an observed data summary and a value more extreme, given a
specific mathematical model and hypothesis (usually H0)
Confidence intervals answer the question ....- Anwers'which values of the parameter are
compatible with the data?'
Range in which we're pretty sure the population parameter lies (mean weight of all apples in an
orchard)
Depends on: variation within population of Interest & sample size.
The more varied a population, the bigger the CI (the less precise our estimate)
, confidence range =- Anwers'which other regression lines are compatible with the observed
data?'
prediction range =- Anwers'Where do future observations with a given x coordinate lie?'
much broader than confidence range
R^2 in multiple linear regression- Anwerssquared correlation between the fitted values. It
measures the proportion of the response's variability that's explained by the ensemble of all
covariates.
always increases when new variables are added; that doesn't mean the model improved.
adjusted R^2 is a better estimation!
adjusted R^2 does what...- Anwerspenalises for additional variables if they don't improve the
model. Thus it may decrease when new variable is added
Binary covariates- Anwerscovariables that can only attain value 0 or 1. If there's only one binary
variable in the model, there's only 2 predicted outcomes.
Factor covariates- Anwersconverting a factor with k levels into k dummy variables.
x=1 if observation is in a certain group
x=0 if obs. is not in certain group
This way each of the covariates can be included in the model as a binary variable.