Week1 - C - Notation

Question 1

i = 1,2,…..,n

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

Answer 1

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

Question 2

n _______ of the p explanatory ________

Answer 2

n observations of the p explanatory variables

Question 3

Notation

y₁, y₂, ….. , y_n

_ observations of the _______ variable

Answer 3

Meaning

n observations of the dependent variable

Question 4

Notation

Answer 4

Meaning

Mean value of dependent (y) variable

Question 5

Notation

Answer 5

Meaning

Mean value of the x_kth explanatory (independent) variable

Question 6

Notation

Answer 6

Meaning:

Parameters of the regression line for the entire population

Question 7

Notation

Answer 7

Meaning

Question 8

Notation:

Answer 8

Meaning:

Error term for the ith observation in the population

Question 9

Notation:

e_i

Answer 9

Meaning:

Error term for the ith observation in the sample.

Question 10

Meaning:

Answer 10

Notation:

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

This is obainted by evaluating the regression funcation at x_i

Question 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 11

Answer:

Question 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 _________.

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 probability distribution as the others and all are mutually independent.

Question 13

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

Answer 13

Answer:

Question 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 _________.

Answer 14

• 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.

Question 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 _______.

Answer 15

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.

Question 16

Question to be formulated confidence interval of regression line.

Answer 16