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Parameter
a numeric quantity that describes an important feature of a population always depend on the model selected to describe the population TERM 2
Statistic
DEFINITION 2 a quantity calculated from a sample that describes an important feature of that sample random variable TERM 3
Estimator
DEFINITION 3 a statistic used to estimate an unknown parameter of a population random variable want estimators to have accuracy and precision TERM 4
Accuracy
DEFINITION 4 closeness to true value classical statistics tends to measure accuracy through the concept of unbiasedness Unbiased estimator: when the expected value is equal to the parameter of interest TERM 5
Precision
DEFINITION 5 reproducibility of measurements In statistics, precision looks at the variance of the estimator an estimator is more precise if its sampling distribution has a smaller standard error
Point
Estimators
estimate specific values of a parameter xbar and s^ estimate mu and sigma^2 respectively most point estimates are continuous random variables, and therefore, have no chance of being correct...instead we use interval estimates TERM 7
Interval Estimates
DEFINITION 7 width of the interval should reflect two factors: 1. confidence in the interval 2. the variability of the estimator confidence refers to the reliability of the procedure, not the specific interval intervals are based on the t-distribution TERM 8
Sample Size
DEFINITION 8 to obtain the desired precision in a study n can be chosen so that the confidence interval is as small as desired. n>/= ((z_alpha/2*sigma/B))^2 Where B is the desired precision we round n up since n must be an integer TERM 9
Type I error
DEFINITION 9 rejecting a true null hypothesis represented by alpha often called the significance level of the test typically worse than type II TERM 10
Type II
error
DEFINITION 10 failing to reject a false null hypothesis represented by Beta often called the power of the test
Inference for a Single Proportion
we need np>/= 5, and n(1-p)>/=5...preferably both greater than/equal to ten TERM 17
Two Sample t-Test
Assumptions
DEFINITION 17
- the distributions of the amounts for both samples are reasonably normal 2. two random samples are independent
- variances for each day are the same TERM 18
Models
DEFINITION 18 express the relationships among variables TERM 19
Independent Variables
DEFINITION 19 usually called regressors or predictors used to try to predict the response or dependent variables TERM 20
Observational Studies
DEFINITION 20 observation of a process no experimenter influence
Designed Experiments
manipulation of the regressors or factors with a measured response TERM 22
Simple Linear Regression
DEFINITION 22 single regressor (x-axis), single response (y-axis) first step...scatterplot TERM 23
Least Squares Estimation
DEFINITION 23 y_i = B_0 + B_1x_i + error B_0 is the intercept B_1 is the slope Assumptions: 1. random errors are independent 2. random errors have mean 0 and variance sigma^ TERM 24
B_
DEFINITION 24 =0...response does not depend on the regressor...response and regressor are uncorrelated 0...values of response grow larger as the values of the regressor are increased....positively correlated TERM 25
Residuals
DEFINITION 25 the differences between the observed and predicted values for the response an appropriate measure of the quality of the fit negative residual- point below line zero residual- point on line (good fit) positive residual- point above the line e_i = y_i
Variance Inflation Factor
(VIF)
allows us to look at the joint relationships among a specified regressor and all the other regressors VIF greater than or equal to 10 indicates a strong problem with collinearity 5 TERM 32
Collinearity Corrections
DEFINITION 32 more data collection (collect data in areas missed before) subset models (assume that because the regressors are highly related we do not need all of them in the model) biased regression methods (think all the regressors are important and should appear in the model)
