Data science quiz 11/4

t-statistic represents

how many standard errors the estimate is from zero

omitted variable bias

• arises when a relevant variable is left out

• a correctly specified model should reflect a plausible set of assumptions and should be complete

• very hard to detect OVB

A model with a higher R² means

the model explains more of the variance in the dependent variable

data mining

• selectively reporting significant results

• scouring through datasets for (partial) correlations from which to develop a thesis

how can outliers and violations of normality affect statistical inference

outliers and non-normal data can distort estimates and invalidate hypothesis tests. Check residual plots, use transformations, or robust methods

consider a regression output where R² = 0.85 and TSS = 1000, what is the ESS?

ESS = R² x TSS = 0.85 × 1000 = 850

three main types of distributional tests

• seeing where a value fits within a distribution (determines how unusual or typical a single value is compared to the rest of the data)

• making a certainty estimate from a sample to the general population (estimating population parameters from a sample, larger the sample the better our estimates)

• comparing two sample means (involves testing whether two groups are significantly different from each other)

z-score

number of standard deviations away from the mean

confidence intervals

error bars, for example at the 95% confidence interval, it is the range of values that has a 95% probability of containing the measure you are interested in

standard error formula

standard deviation of the sample mean

what question do we answer with a t test

is the difference between the two statistically significant?

what are all the explanations of correlation between A and B?

A causes B (possibly through C)

B causes A (possibly through C)

C causes both A and B

C causes B, and A is only spuriously correlated

What other misspecifications could there be to a set of data?

• omitted variable bias

• included variable bias

• normality and outliers

• data mining

• interaction effects

• casual endogeneity

• ecological fallacy

included variable bias

the addition of multiple (usually irrelevant) variables to obtain the desired result

normality and outliers 

• OLS can only analyze variables that follow a (close to) normal distribution - data can still be transformed 

• make sure you eliminate outliers

How is the margin of error affected by sample size

The margin of error decreases as the sample size increases.

inferential statistics

using sample data to make inferences about a larger populationd

distributional tests

statistical tools that help determine how data points relate to theoretical probability distributions

OLS (ordinary least squares) multivariate analysis

statistical technique used to estimate the relationship between one dependent variable and two or more independent variables, extension of a simple linear regression

R² formula

1 - (residual sum of squares / total sum of squares)

TSS (total sum of squares)

• measures the total variation in the dependent variable

• quantifies how spread out the observed data are before considering any model

ESS (expected sum of squares)

• a quantity used in describing how well a model, often a regression model, represents the data being modelled

RSS (residual sum of squares)

• measures the unexplained variation

• difference between point and line of best fit