Week1 - C - Notation Flashcards Preview

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

i = 1,2,…..,n

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

A

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

2
Q

n _______ of the p explanatory ________

A

n observations of the p explanatory variables

3
Q

Notation

y1, y2, ….. , yn

_ observations of the _______ variable

A

Meaning

n observations of the dependent variable

4
Q

Notation

A

Meaning

Mean value of dependent (y) variable

5
Q

Notation

A

Meaning

Mean value of the xkth explanatory (independent) variable

6
Q

Notation

A

Meaning:

Parameters of the regression line for the entire population

7
Q

Notation

A

Meaning

8
Q

Notation:

A

Meaning:

Error term for the ith observation in the population

9
Q

Notation:

ei

A

Meaning:

Error term for the ith observation in the sample.

10
Q

Meaning:

A

Notation:

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

This is obainted by evaluating the regression funcation at xi

11
Q

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

A

Answer:

12
Q

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 _________.

A

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
Q

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

A

Answer:

14
Q

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 _________.
A
  • 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
Q

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 _______.

A

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
Q

Question to be formulated confidence interval of regression line.

A