data analysis final

correlation coeffeicient

measurement of the strength of a linear relationship between two variables

interpolation

predicting y values for values that are between the x values in the dataset

extrapolation

predciting y values for x values that are beyond the values in the dataset

coefficient of determination / R²

the ratio of how much one variable explains the variation

MSE

what can you use as an estimate of variance for significance testing

t test

tests for a significant regression relationship

f test

tests the regression model for statistical significance

adjusted R²

ratio of explained variation in the regression model that accounts for the number of predictor variables in the model

multicollinearity

when two predictor variables high a high linear correlation

VIF > 10

how do you determine serious multicollinearity?

VIF > 4

how do you determine potential multicollinearity?

confidence intervals around a mean response

measures the accuracy of the mean response of a population, constructed around a predicted value of Y at a given value of X

prediction intervals for an individual response

measures the accuracy of a single individual’s predicted response

larger

is the standard error of a prediction interval for an individual response larger or smaller than the standard error of E[y|x]?

analysis of variance

statistical models used to analyze the differences amongst group means and amongst the associated procedures with each

dummy variables / indicator variables

variables representing a non-numerical response by encoding the responses into numbers

K - 1 rule

the number of dummy variables needed to represent a categorical variable with K levels

not different from reference variable

what does a high p value mean when using dummy variables?

mean centering

model where the intercept is centered around the mean of the predictors instead of when the predictors = 0

interaction terms

statistical test evaluating whether a variable has the same or a different effect (slope) across different dummy variables

curvilinear relationship

relationship between variables where the effect is not a straight line, requiring the use of a polynomial term in the regression equation

residuals plot is non-linear/curved

when is there a curvilinear relationship?

simple first order model with one predictor variable

regression modeling a linear relationship with one predictor variable

second order model with one predictor variable

regression modeling a curvilinear relationship with one predictor variable

linearity, independence, normality, constant variance

what are the 4 core assumptions of a valid regression model?

independence

assumption that each residual error term is independent of the others

normally distributed, randomly scattered around 0, constant spread from left to right, no obvious patterns

what are the 4 factors considered when checking residuals?

homoscedasticity

residuals display a constant, even band of variance across all fitted values

heteroscedasticity

residuals are fanned out, funneled, contract, or have a shape, indicating non constant error variance

logarithmic transformation, power transformation

what are the two transformations used on the response variable to fix heteroscedasticity?

time ordered, clustered data, repeated measures

what 3 qualifications prove that data points are not independent?

time ordered

observations of independent data should not be sequential over time

clustered data

observations of independent data should not be similar geographically or organiziationally/companies

repeated measures

observations of independent data should not be repeated measurements of the same subject

influential observation / outlier

observation that has a disproportionate affect on the slope and Y-intercept in regression

leverage

how much an observation influences the model

standardized residuals

residuals scaled by the overall model’s variability so you can compare residuals accross observations

studentized residuals

residuals scaled using the error estimate excluding that particular observation, which is better for detecting outliers

cook’s distance

measure of how much the regression model will change if you remove one observation

collect more data near that point, use transformations, remove the point

what 3 methods can you use to handle outliers?

D > 4/n

when do you remove an influential point from data?

reg = lm(y ~ x, data = df)

what is the R syntax for lienar regression

abline(reg, col = “red”)

what is the R syntax for adding a regression line to a graph

res = reg$residuals

what is the R syntax for finding residuals

str(variable)

what is the R syntax for checking variable types

variable = factor(variable)

what is the R syntax forcreating dummy variables

qq plot

plot of residuals telling us if residuals are normally distributed. should be a relatively straight, diagonal line

the sum of each data point minus the mean

how do you find the mean center of a variable?

parsimonious model

relatively simple regression models with few predictor variables and relatively high R²

forward selection

model selection method adding one predictor at a time to an intercept only model as long as there is a significant reduction in the residual SSE. variables cannot be removed once added

backward elimination

model selection method removing one predictor at a time from a full model based on P-values. variables cannot be added again once removed.

best subsets regression

model selection method evaluating every combination of predictors and selects the best model based on a chosen criterion, like BIC or R². gives the lowest error

plot()

what is the R script for generating four diagnostic plots?

vif()

what the R script for the variance inflation factor?

stepwise regression

hybrid model selection method that can both add remove variables at each step. starts with an intercept only model

heuristics

procedures that are one variable at a time, such as stepwise regression, forward selection, or backward elimination

Marlows CP

model selection criterion that compares a reduced model to the full multiple model to see if the model has enough predictors without overfitting

lowest CP

how do you select a model using marlows CP?

akaike information criterion / AIC

model selection criterion that balances model fit and complexity by judging the amount of information lost by a given model while penaliziing for number of predictors. focuses on best fit

Bayesian information criterion / BIC

model selection criterion that evaluates a model's fit while adjusting for the number of predictors, used to prevent overfitting. tends to pick simplest model

lowest BIC

how do you select a model using BIC?

lowest AIC

how do you select a model using AIC?

step()

what is the R script for stepwise regression?

regsubsets()

what is the R script for best subsets regression?

qqplot(reg)

what is the R script for qq plot?