Week1 - C - Notation Flashcards Preview

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Flashcards in Week1 - C - Notation Deck (16)
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1

i = 1,2,.....,n

 

i refers to the ith _________ or record in a data set of records.

i refers to the ith observation or record in a data set of records.

2

n _______ of the p explanatory ________

n observations of the p explanatory variables

3

Notation

y1, y2, ..... , yn

 

_ observations of the _______ variable 

Meaning

n observations of the dependent variable 

4

Notation

 

Meaning

 

Mean value of dependent (y) variable

5

Notation

 

 

Meaning

 

Mean value of the xkth explanatory (independent) variable

6

Notation

 

 

Meaning:

 

Parameters of the regression line for the entire population

7

Notation

Meaning

8

Notation:

Meaning:

 

Error term for the ith observation in the population

9

Notation:

ei

Meaning:

Error term for the ith observation in the sample.

10

Meaning:

 

 

Notation:

 

Estimated value of y for the ith observation in a sample.

 

This is obainted by evaluating the regression funcation at xi

11

If we want to build a linear regression model for population with one independent variable and one dependent variable express the the valid relation

 

Hint:  Simple Linear Regression

Answer:

 

 

12

In probability theory and statistics, a collection of random variables is independent and identically distributed (iid) if each random variable has the same __________ _______ as the others and all are mutually _________

In probability theory and statistics, a collection of random variables is independent and identically distributed (iid) if each random variable has the same probability distribution as the others and all are mutually independent

13

Express the model we are going to build since we do not know the Beta's or Sigma.

 

 

Answer:

14

In the following display:

 

  • The slope of the regression line is _____
     
  • The intercept is _______
     
  • The errors are assumed to be ______ ______ with mean of ____ and standard deviation _____ across all the values of _.
  • This constant sigma is also called _________.

  • The slope of the regression line is beta 1
     
  • The intercept is beta 0
     
  • The errors are assumed to be normally distributed with mean of zero and standard deviation sigma across all the values of x.
  • This constant sigma is also called homoscedasticity.

15

In statistics, a sequence (or a vector) of random variables is homoscedastic /ˌhoʊmoʊskəˈdæstɪk/ if all its random variables have the same _____ ________

 

So, homoscedasticity literally means“ having the same _______.

n statistics, a sequence (or a vector) of random variables is homoscedastic /ˌhoʊmoʊskəˈdæstɪk/ if all its random variables have the same finite variance

 

So, homoscedasticity literally means“ having the same scatter.

16

Question to be formulated confidence interval of regression line.