100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Summary of Statistics II: Applied Quantitative Analysis $6.98
Add to cart

Summary

Summary of Statistics II: Applied Quantitative Analysis

 15 views  0 purchase
  • Course
  • Institution

Summary of Statistics II: Applied Quantitative Analysis

Preview 3 out of 16  pages

  • August 10, 2022
  • 16
  • 2019/2020
  • Summary
avatar-seller
1. Comment
3 February 2020 at 13:28:35
Using b0 and b1 instead of a and
b allows us to work with multiple
variables (b3, b4, etc)

2. Comment
3 February 2020 at 14:11:15
Simple linear regression model

3. Comment
3 February 2020 at 13:34:43
Expected value (ignoring error) of y
given x

4. Comment
3 February 2020 at 13:36:18 Lecture 1: Introduction to regression analysis
Difference between points and line
(error i) Regression is related to correlation, but:
• Can estimate impact of multiple independent variables
5. Comment
• Not just strength of association, but size of effect
3 February 2020 at 13:28:35
• Can assess null hypothesis
Using b0 and b1 instead of a and
• Assumes linear correlation
b allows us to work with multiple
variables (b3, b4, etc)
Regression line
• Formula:
6. Comment
3 February 2020 at 14:12:40 • y = a + bx
Elaborate on web lecture
1 • ŷi = b0 + b1xi
• "Line of best t”: minimizes distances between points and line
• ^: estimate
• i: observation number (obs.1, obs.2, etc)




2 yi = b0 + b1xi + i

• i: error
• Mean = 0, variance = σ2 (only if y-variable is normally distributed)

3 Alternative formula: E[yi|xi] = b0 + b1xi

Ordinary Least Squares (OLS): method for finding regression line
4 • Minimizes sum of squared residuals
(yi − yî )2 = (yi − b0 − b1 xi )2
• Squared residuals: SSR = ∑ ∑
5 • Plug values into formula (ŷi = b0 + b1xi ) to find regression line
• Find b̂1 using SPSS
• b0̂ = ȳ − b1̂ x̄

Regression assumptions:
6 • Relationship between E[yi|x] and x is linear and additive
• E[ i|x] = 0




𝜀𝜀 fi 𝜀

,7. Comment
3 February 2020 at 14:14:42
Non-negative numbers (e.g. #
wars)

8. Comment
3 February 2020 at 15:02:02
Categorical/ordinal (named)




• Variables suited for regression:
• Dependent variable must be interval ratio, otherwise:
• If nominal/ordinal: logistical regression
7 • If count scale: Poisson and negative binomial regression (not in course)
• Explanatory variables can be any type
• Variance ≠ 0




Lecture 1: SPSS

Find b̂1:
[Analyze] → (Correlate] → [Bivariate…] → [Options…] → select “Cross-product deviations and
?
covariances” → [Continue] → [Paste] → click play → b1̂ =
?




Recode variable → different variables:
[Transform] → [Recode into Different Variables] → drag variable into box → [Old and New
8 Values…] → input relevant instructions → (select “Output variables are strings” if necessary) →
[Continue] → select variable → input new label → [Change] → [Paste] → click play

Add regression line to scatterplot:
Double-click graph in output viewer → [Elements] → [Fit Line at Total]

Select cases (multiple conditions):
[Data] → [Select Cases…] → select “If condition is satisfied” → [If…] → input conditions (“|”
between each full equation) → [Continue] → [Paste] → click play

, 9. Comment
10 February 2020 at 16:29:47
Produces random errors

10. Comment
10 February 2020 at 16:24:22
I.e. consider sampling error to
express uncertainty

11. Comment
10 February 2020 at 16:44:30
Since b̂ 1 is normally distributed

12. Comment
10 February 2020 at 16:28:32
SEb depends on SSr
Lecture 2: Simple Linear Regression Analysis
13. Comment
10 February 2020 at 16:40:19
9 Regression line of sample ≠ regression line of population
# explanatory variables (b1, b2,
b3, etc)

14. Comment Signi cance testing of regression line
10 February 2020 at 16:33:20 10 (Use inference to get to population parameter)
b̂ 1 is more precise
Use SPSS to generate values needed for following instructions.

11 T-test:
b̂ b1

t̂ = →t =
12
̂ b)̂
se( SEb1
• H0: b1 = 0
• H1: b1 ≠ 0
13 • df = n - p - 1
14 • Variance of b̂1 is lower if:
• X has high variance
• N is large
• has low variance (low SSR)
MSR
SÊ b1 =
• SSX
• MSR = mean square of residual
• SSX = sum of square of X variable
• Alternative:




• B: unstandardized regression coefficient




𝜀

fi

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 bellakim. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $6.98. 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
$6.98
  • (0)
Add to cart
Added