GW Blok 6 Seminar 4.1 Simple linear regression including hypothesis testing for regression coefficients

0.0(0)
studied byStudied by 0 people
GameKnowt Play
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
Card Sorting

1/6

encourage image

There's no tags or description

Looks like no tags are added yet.

Study Analytics
Name
Mastery
Learn
Test
Matching
Spaced

No study sessions yet.

7 Terms

1
New cards

What is the best estimate?

<p></p>
2
New cards

What is simple linear regression?

  • To determine whether the slope coefficient β1​ is significantly different from zero.

    • H0 = β1 = 0

    • Ha = β1 ≠ 0

  • β1 = 0 → variables X does not explain any linear variation in Y, the variables are not related → horizontal line

  • To test if the slope is significantly different from zero at population level, use CI, p-value or t-statistic

3
New cards

What are the assumptions in linear regression?

  1. Linear relation between X and Y

  2. Independent observations

    1. Body temperature and age is observed per person → implies independence

  3. Constant variance of Y for the whole range of X

    1. Those are the conditions to be met, but we don’t test this during the exam

  4. For any value of X, Y is normally distributed

    1. Those are the conditions to be met, but we don’t test this during the exam

Then β1 hat follows an approximately normal distribution or t-distributed with n-2 degrees of freedom

<ol><li><p>Linear relation between X and Y</p></li><li><p>Independent observations</p><ol><li><p>Body temperature and age is observed per person → implies independence</p></li></ol></li><li><p>Constant variance of Y for the whole range of X</p><ol><li><p>Those are the conditions to be met, but we don’t test this during the exam</p></li></ol></li><li><p>For any value of X, Y is normally distributed</p><ol><li><p>Those are the conditions to be met, but we don’t test this during the exam</p></li></ol></li></ol><p>Then β<sub>1 hat</sub> follows an approximately normal distribution or t-distributed with n-2 degrees of freedom</p><p></p>
4
New cards

What is the difference between the population regression model and the sample regression line?

knowt flashcard image
5
New cards

How is the error variance σ2 estimated in regression?

knowt flashcard image
6
New cards

Why should you always plot your data before running a regression?

Because visual inspection can reveal outliers, nonlinear patterns, heteroscedasticity, and data errors that summary statistics might miss.

7
New cards

What are residuals in regression?

<p></p><p></p>