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
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
Voordelen van het kopen van samenvattingen bij Stuvia op een rij:
Verzekerd van kwaliteit door reviews
Stuvia-klanten hebben meer dan 700.000 samenvattingen beoordeeld. Zo weet je zeker dat je de beste documenten koopt!
Snel en makkelijk kopen
Je betaalt supersnel en eenmalig met iDeal, creditcard of Stuvia-tegoed voor de samenvatting. Zonder lidmaatschap.
Focus op de essentie
Samenvattingen worden geschreven voor en door anderen. Daarom zijn de samenvattingen altijd betrouwbaar en actueel. Zo kom je snel tot de kern!
Veelgestelde vragen
Wat krijg ik als ik dit document koop?
Je krijgt een PDF, die direct beschikbaar is na je aankoop. Het gekochte document is altijd, overal en oneindig toegankelijk via je profiel.
Tevredenheidsgarantie: hoe werkt dat?
Onze tevredenheidsgarantie zorgt ervoor dat je altijd een studiedocument vindt dat goed bij je past. Je vult een formulier in en onze klantenservice regelt de rest.
Van wie koop ik deze samenvatting?
Stuvia is een marktplaats, je koop dit document dus niet van ons, maar van verkoper bellakim. Stuvia faciliteert de betaling aan de verkoper.
Zit ik meteen vast aan een abonnement?
Nee, je koopt alleen deze samenvatting voor €6,49. Je zit daarna nergens aan vast.