100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Summary Statistics II: Applied Quantitative Analysis $13.97
Add to cart

Summary

Summary Statistics II: Applied Quantitative Analysis

 5 views  0 purchase
  • Course
  • Institution

In this document you will be able to understand the basic terms of statistics II. It is included everything you need to know for the exam. Using these notes I got a 7.5 in the multiple choice exam.

Preview 3 out of 25  pages

  • April 8, 2022
  • 25
  • 2021/2022
  • Summary
avatar-seller
Week 1- Bivariate Linear Regression
I. Models
Models
= Models are statistical abstractions
● They enable us to make predictions, summarize relationships, and test causal claims in a
sample of data
● Provided some further assumptions hold, they also let us extrapolate claims to a broader
population
● Basic structure of a model: data = model + error
● We want a model that most efficiently and accurately describes the data...although these goals
can be in tension!

Usage of models – We use statistical models to explore associations and summarize relationships
between variables

Types of Regression Model
● Ordinary least squares (OLS): Modeling continuous dependent variables
● Logit models: Modeling binary outcome variables
● Multinomial and ordered/ordinal logit models: Modeling categorical and ordinal dependent
variables


II. Linear Regression
Types of Variables
1. The variable we want to predict/explain/understand (Y)
● Dependent variable
● DV
● Outcome variable
2. The variable we’re using to predict/explain the outcome (X)
● Independent variable
● IV
● Predictor variable
● When we add additional variables to the model: control variables; covariates; X1, X2; Z

Regression Line
The simplest model we can use is a straight line, which we can
represent via this formula:
y = a + bx
● a = the constant/intercept
● b = the slope of the line

Constant/intercept
If X = 0, what value should we expect Y to be on average according to the model?
Here: 51




1

,Slope
Slope or b – How should we expect Y to change on average for each one unit change in X according to
the model?
Here: 0.62.

Error/Residual
Difference between what the model predicts and the observed value;
they are prediction errors

The sample Regression Equation
● b0 = the constant/intercept = average or (expected) value of Y when X =0 in our data
● b1 = slope of the line = average change in Y given a one unit change in X in our data
● εi = residual error

Which one is the best line? – The one that explains the data best.

OLS – Least Squares Regression Models
OLS – The regression line that minimizes the sum of the squared residuals (SSR) or sum of squared
prediction errors




III. Interpreting Coefficients and Making Predictions
Types of Independent Variable in OLS
● Statistics I: Tests depending on nature of independent (and dependent) variable
○ Continuous DV and indicator/binary IV: t-test
○ Continuous DV and nominal IV: ANOVA
○ Continuous DV and IV: correlation
● Linear Regression:
○ DV – continuous
○ IVs – binary, continuous, nominal, or ordinal
● Logistic and Multinomial Logistic Regression for
○ DV – Binary/Nominal

Coefficients
Bivariate regression for continuous variables




Bivariate Regression Coefficient and Correlation Coefficient
The bivariate regression coefficient is an unstandardized version of the correlation coefficient




2

, ➔ Formula to calculate coefficient

The Constant or Y-Intercept Term
The constant or y-intercept term estimates the average value of Y when X = 0
● Example – Model with just ideology: The constant (= 3.979) indicates the average value of Y
when Ideology = 0. Here: respondents with the most left-wing self-placement on the ideology
scale

Two Cautions about the Constant
1. Don’t interpret the slope coefficient as saying something about the constant
● Mistake: “In model 1, it can be seen that a 1 unit increase of [the IV] leads to a 0.114 unit
increase of the constant”
● The constant gives the mean value of the DV when X = 0; the slope for an IV tells us how Y
changes on average for each one unit increase in X
2. Values for b0 (the constant) may not be that meaningful if the IV(s) cannot/does not take on a score
of 0
● As a general rule, we probably don’t care all that much about what specific value the constant
takes beyond its use in calculating predictions from the model

Predictions
The regression equation enables us to describe the relationship between an IV and a DV
via the slope coefficient (b1)
The regression equation also enables us to make specific predictions for what value we should expect Y
to take on for any given value of X


IV. Coefficients and Inference
From Description to Inference
● The coefficients in our regression model summarize or describe the relationship between X and
Y in our data/sample
● We can also use other output from the model (e.g., standard errors) to make inferences to an
underlying population (contingent on some assumptions)




3

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller martajordnban. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $13.97. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

52510 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling

Recently viewed by you


$13.97
  • (0)
Add to cart
Added