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isye 6414 midterm 1 study notes questions and answers
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isye 6414 midterm 1 study notes"All models are wrong, _________________" - questions and answers-but some are useful
Are linear models a true representation of reality? - questions and answers-no
assumptions of simple linear regression - questions and answers--linearity/mean zero
assumption
-constant variance assumption
-independence assumption
-normal distribution of error
can residual analysis check independence assumption? - questions and answers-no, all that
can be assessed with residual analysis is uncorrelated errors.
confidence interval - questions and answers-provides an interval estimate for the true average
value of y for all instances of a particular x
constant variance assumption - questions and answers-the variance (σ-squared) of the error
terms or deviances is constant
correlation coefficient - questions and answers-a statistic that efficiently summarizes how well
the Xs are linearly related to y
the square of the correlation coefficient is R-squared: p² = R²
data structure of simple linear regresion - questions and answers-pairs of data - one response
variable value, one predicting variable value
estimated regression line - questions and answers-average estimated mean response for all
settings of the predicting variable
estimation uncertainty source - questions and answers-parameter estimation
fitted values - questions and answers-ŷ_i = B̂₀ + B̂₁(x_i)
regression line where the parameters are replaced by their estimated values
fixed variable - questions and answers-does not change with the response, but is set before the
response is measured
, hat - questions and answers-differentiates between estimated parameters and the true
parameters
how do we check normality? - questions and answers-- quantile plot/normal probability plot -
should be a straight line
- histogram - should be symmetric, unimodal, no gaps
- use both!
how do we diagnose the assumptions? - questions and answers-evaluate the residuals
(differences between observed and fitted responses -- this is NOT error term because we don't
actually know β₀ and β₁) by plotting them against both fitted and predictive values and checking
if the scatter plot is random around the zero line (it should be!)
if the assumptions don't hold up.... - questions and answers-the regression could still be useful
with some transformation of y or x.
independence assumption - questions and answers-response variables are independently
drawn
responses are not related to each other (unlike in time series)
influential points - questions and answers-data points far from the mean of x or y data that
influence the regression model fit significantly
- change estimated parameter values
-change significance
-change sign
-etc.
large |t-value| - questions and answers-reject the null hypothesis
leverage points - questions and answers-data points far from the mean of x data
Linearity/Mean zero assumption - questions and answers-Means that the expected value
(deviances) of errors is zero
mean squared error - questions and answers-(sum of squared residuals) / (n-2)
δ_hat² --> estimator for δ²
multiple linear regression - questions and answers--more than one predicting variable
-estimate the relationship with a plane
y= β0 + β1(x1) + β2(x2) + ε
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