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What is the linear Model
- ŷ = bo + b1 x
- bo is intercept and b1 is slope
- find this by using least squares method
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Lest Squares Method
- b1 = Sy/Sx and b0= Y-bar - b1x̅
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What is a Residual
- difference between the observed value and what the model predicts
- e = y-ŷ Residual = observed - predicted
- also: y = ŷ + e
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Linear Regression
Way to model the relationship between two quantitative variables with a line
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scatterplot
shows relationship between quantitative variables.
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Explanatory Variable
causal variable on the x-axis
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Leverage Point
- Outlying in X-values
- is influential
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parameter and statistics
- parameter: unknown population quantities
- Statistics computed from a sample are used to estimate parameters which describe a population.
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Simple Random Sample
every possible sample of size n has the same chance of being selected
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Stratified Random Sample
divide area into subareas and then take a simple random sample within those subareas
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Systematic Random Sample
involves sampling every kth unit in an ordered list of the units in the population
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Cluster Sampling
random sample of clusters of individuals, and then survey every indidual
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Multistage Designs
situations when using more than 1 sampling mehtod
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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
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Response Variable
- Effect variable
- on the Y-Axis
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Observational Study
- The researcher only observes to collect data
- no manipulation
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Retrospective Studies
- The response variable is already known
- the explanatory variable is collected by looking at past histories of subjects
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Prospective Studies
Explanatory Variable is observed about subjects, and then they are followed into the future to see response variables
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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
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Factors and levels
in an experiment, a factor is usually a categorical explanatory variable, and the levels are the different possible values
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elements for a good experiment
- Necessary: comparison, randomization, Replication
- Other: Placebo, Blindness
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