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What is the linear Model
 ŷ = b_{o }+ b_{1 }x
 b_{o} is intercept and b_{1} is slope
 find this by using least squares method

Lest Squares Method
 b_{1} = ^{S}^{y}/S_{x }and b_{0}= Ybar  b_{1}x̅ ^{}

What is a Residual
 difference between the observed value and what the model predicts
 e = yŷ Residual = observed  predicted
 also: y = ŷ + e

Linear Regression
Way to model the relationship between two quantitative variables with a line

scatterplot
shows relationship between quantitative variables.

Explanatory Variable
causal variable on the xaxis

Leverage Point
 Outlying in Xvalues
 is influential

parameter and statistics
 parameter: unknown population quantities
 Statistics computed from a sample are used to estimate parameters which describe a population.

Simple Random Sample
every possible sample of size n has the same chance of being selected

Stratified Random Sample
divide area into subareas and then take a simple random sample within those subareas

Systematic Random Sample
involves sampling every k^{th} unit in an ordered list of the units in the population

Cluster Sampling
random sample of clusters of individuals, and then survey every indidual

Multistage Designs
situations when using more than 1 sampling mehtod

What are the Sampling Bias's
 Nonresponse
 Interviewer Bias  The teacher personally asking students about the class, or only asking certain groups known of having a certain opinion
 Question Wording

Response Variable
 Effect variable
 on the YAxis

Observational Study
 The researcher only observes to collect data
 no manipulation

Retrospective Studies
 The response variable is already known
 the explanatory variable is collected by looking at past histories of subjects

Prospective Studies
Explanatory Variable is observed about subjects, and then they are followed into the future to see response variables

Experiment
 Researcher assigns the explanatory variable for each unit
 a cause and effect relationship can be established
 if conducted properly the lurking variable can be minimized

Factors and levels
in an experiment, a factor is usually a categorical explanatory variable, and the levels are the different possible values

elements for a good experiment
 Necessary: comparison, randomization, Replication
 Other: Placebo, Blindness

