midterm 1

Question 1

Three Criteria for Causality

Answer 1

1. Plausibility
2. Time Order
3. Non-Spuriousness

Question 2

What are the two type of variables?

Answer 2

Numeric and Categorical

Question 3

mean, median, mode

Answer 3

1. mean: every number added up divided by how many numbers
2. median: middle
3. mode: most common

Question 4

Range

Answer 4

maximum – minimum value

Question 5

IQR

Answer 5

Q3 – Q1 (50% of the data)

Question 6

standard deviation is what square rooted?

Answer 6

variance

Question 7

Cluster Sample vs Stratified Sample

Answer 7

Cluster: randomly samples existing clusters, then samples within those clusters

Stratified: creates subgroups based on variables and samples from within those subgroups

Question 8

68 – 95 – 99.7 rule for normal distribution

Answer 8

68% of data will fall within 1 sd of mean
95% of data will fall within 2 sd of mean
99.7% of data will fall within 3 sd of mean

Question 9

how to calculate ANOVA
Test Statistic:

Answer 9

𝑀𝑒𝑎𝑛 𝑆𝑞𝑢𝑎𝑟𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝐺𝑟𝑜𝑢𝑝𝑠 (𝑀𝑆𝐺)/ 𝑀𝑒𝑎𝑛 𝑆𝑞𝑢𝑎𝑟𝑒𝑑 𝐸𝑟𝑟𝑜𝑟 (𝑀𝑆𝐸)

Question 10

What does MSG conceptually mean?

Answer 10

the amount of variation between groups. In other words, how much of the variation you see in the sample is because there are multiple groups.

If this number is high, it means that the groups are different from each other. If this number is low, it means that the group means are all very similar to the overall mean – the groups are NOT different.

Question 11

What is MSE conceptually?

Answer 11

the amount of variation within groups. If this number is high, it means that there is a lot of variation within the groups. If this number is low, it means that all of the observations are pretty close to average for their group.

Question 12

Factorial ANOVA

Answer 12

A technique for studying the effect of two or more categorical independent variables on a numeric dependent variable accounting for interaction effects among the independent variables

Question 13

Main Effect

Answer 13

The overall relationship between an independent and a dependent variable

Question 14

Interaction Effect

Answer 14

when the relationship between two variables is different depending on the value of a third variable

Question 15

Tukey HSD (factorial anova)

Answer 15

This tests every pair to see if they are statistically significantly different

In R: TukeyHSD() function on the aov model object

Question 16

multivariate

Answer 16

studies relationships of independent variables with multiple dependent variables

Question 17

conditions for regression

Answer 17

1. linearity
2. nearly normal residuals
3. constant variability
4. independent observations

Question 18

coefficient vs y-intercept

Answer 18

coefficient: Bx or mx
y-intercept: Bo

Question 19

RMSE root mean square error (three steps)

Answer 19

1. find squared error
2. calculate mean of the se
3. take the square root

Question 20

what minimizes the RMSE?

Answer 20

the mean, and the line that minimizes RMSE is the best fit line - OLS (ordinary least squares)

Question 21

R for regression

Answer 21

summary(lm(depedent variable ~ indepepdnet variable, data = dataset))

Question 22

high leverage vs influencial point

Answer 22

high leverage: very high or low value on the independent variable (x)

influencial point: extreme in both independent (x) and dependent (y) variables

Question 23

Simpson’s Paradox

Answer 23

where the observed relationship b/w two variables changes when the population is divided into different groups

Question 24

Adjusted R squared in multiple regression

Answer 24

applies a penalty based on the number of parameters in the model

Bo + B1 = two parameters
Bo + B1 + B2 = three parameters

Question 25

How to Build a Multiple Regression Model

Answer 25

1. Simultaneous Inference or Full Entry: put all variables into model 2. Hierarchical: adding variables in a pre-specified and theoretically justified order 3. Forward Selection: keep on adding variables 4. Backward Elimination: start with full and eliminate

Question 26

How is ANOVA a special case of regression?

Answer 26

Regression: how much of the variation in Y is explained by variation in the numerical variable X ANOVA: how much of the variation in Y is explained by a categorical variable

Question 27

nominal vs ordinal (categorical variables)

Answer 27

nominal: Data is organized into categories that have no intrinsic order ordinal: Data is organized into categories that have a clear order

Question 28

variable vs case

Answer 28

Variable: A feature that varies across cases/observational units/units of analysis Case: an individual person/object whose features you are measuring and evaluating.

Question 29

4 types of sampling frames

Answer 29

1. Simple random sample: Randomly select a sample from a list 2. Systematic sample: Organize the sampling frame in a list and select every kth individual 3. Cluster Sample: Randomly sample existing clusters (e.g. cities, schools, neighborhoods) first, then sample within those clusters 4. Stratified sample: Create subgroups (called strata) of the sample based on important variables (often race, gender, or other demographic features) and then sample from within those subgroups

Question 30

The Central Limit Theorem (for proportion):

Answer 30

When observations are independent, the sampling distribution of sample proportions for a sample of size n is a normal distribution with a mean of P and a standard deviation of √((𝑝(1−𝑝))/𝑛)

Question 31

parameters vs statistics

Answer 31

parameter (population) P – the population proportion μ (mu) – the population mean σ (sigma) – the population standard deviation statistic (sample) 𝑝 ̂ (p-hat) – the sample proportion 𝑥 ̅ (x-bar) – the sample mean s – the sample standard deviation

Question 32

what's the null hypothesis in linear regression

Answer 32

that the coefficient (B1x) is zero