data analysis
Help!
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| useful graphs | scatterplot
can get a sense for the nature of the relationship
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| what to look for in a graph | relationship between two variables where one variable causes changes to another
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| location | where most of the data lies
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| spread | variability of the data, how far apart or close together it is
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| shape | symetric, skewed etc
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| nature of relationship | existent/ non-existent
strong/ weak
increasing/ decreasing
linear/ non-linear
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| outliers in scatterplots | represent some unexplainable anomalies in data
could reveal possible systematic structure worthy of investigation
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| casual relationship | relationship between two variables where one variable causes changes to another
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| explanatory variable | explains or causes the change
on x-axis
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| response variable | is changed
on y-axis
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| useful numbers | correlation and regression
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| formula for the correlation coefficient | r= 1/(n-1) ∑▒〖((xi-x ̅)/sx〗)((yi-y ̅)/sy)
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| xi or yi | axis values of corresponding letter
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| xbar or ybar | mean of axis values of corresponding letter
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| sx or sy | standard deviation of axis values of corresponding latter
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| properties of r | close to 1 = strong positive linear relatoinship
close to -1 = strong negative linear relationship
close to 0 = weak or non-existent linear relationsip
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| cautions about the use of r | only useful for describing linear relationships
sensitive to outliers
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| regression models | general linear relationships between variables
focus negative = decrease
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| what regression modelling does | describes behaviour of response variable (the variable of interest) in terms of a collection predictors (related variables ie. explanatory variable(s))
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| a linear framework is used to look at? | the relationship between the response and the regressors
formula: Y = α + βx
Where α is the intercept and β is the slope
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| ideal model for linear framework in terms of responses and regressors | one unique response to one given regressor
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| real world model for linear framework in terms of responses and regressors | must approximate
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| statistical model | relates response to physical model predictions
allows for better predictions and quantification of uncertainty concerning the response
to make decisions
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| what does regression analysis do? | finds the best relationship between responses and regressors for a particular class of models
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| experimenter controls predictors, why? | may be important for making inferences about the effect of predictors on response
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| course assumption | predictors are controlled in an experiment or at least accurately measured
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| define a good statistical model | fit, predictive performance, parsimony interpretability
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| qualitative description of model | response = signal + noise
Y = α + βx + ǫ
ǫ = noise
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| define signal | a small number of unknown parameters
variation in response explained in terms of predictors
it is the systematic part of the model
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| define noise | residual variation unexplained in the systematic part of the model
can be described in terms of unknown parameters
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| what does a good statistical model do to possibly large and complex data | reduces it to a small number of parameters
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| a model will fit well if | the systematic part of the model describes much of the variation in the response (low noise)
large number of parameters may be required to do this
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| define parsimony: | smaller number of parameters = grater reduction of data, more useful for making a decision
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| there is a cycle between what? | tentative model formulation, estimation of parameters and model criticism
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| a good model will | manage balance between goodness of fit and complexity
provide reduction useful data
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| model response variable in terms of a single predictor | yn = values of the response variable
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