Deck 3: A Brief Overview of the Classical Linear Regression Model

Question 1

Consider the following graphs.
A. B.
Which of the following statements is true?

A) A is depicts a non-linear relationship between y and x
B) B is depicts a linear relationship between y and x
C) A and B depict linear and non-linear relationships between y and x respectively
D) A and B depict non-linear and linear relationships between y and x respectively

Answer 1

A and B depict linear and non-linear relationships between y and x respectively

Question 2

The derivative of e^4x-2 is:

A) 4/(4x-2)
B) (4x-2)e⁴
C) (4x-2)e^4x-2
D) 4e^4x-2

Answer 2

4e^4x-2

Question 3

Log(1) is:

A) 1
B) 0
C) 2.71828…
D) Undefined

Answer 3

0

Question 4

What is the second order derivative of the function ?

A)
B)
C)
D)

Question 5

The linear relationship between two variables (y and x) can be represented by the equation. Which of the following statements is true? (I) Parameter a is termed the intercept
(II) Parameter a is termed the slope
(III) Parameter b is termed the gradient
(IV) Parameter b is termed the constant

A) I and IV only
B) I and III only
C) II and III only
D) II and IV only

Question 6

If A is of dimension 1 * 4 and B is of dimension 4 * 1, what is the most accurate term to describe the result of the matrix multiplication AB?

A) A scalar
B) A column vector
C) A row vector
D) A matrix

Question 7

The derivative of log(5x) is:

A) 5/x
B) 1/x
C) 5log(x)
D) 5/log(x)

Question 8

Assume that the relationship between a company's stock price (y) and dividends paid per share (x) is linear. If the slope of the equation is 0.50 and the intercept is 30, what would be the expected stock price if the dividend paid was 3?

A) 33
B) 30.50
C) 31.5
D) 30

Question 9

If matrices and, what is AB?

A)
B)
C)
D)

Question 10

The simplest possible way of writing 3x⁵ * 7x³ is:

A) 21 x⁵ * x³
B) 21 x¹⁵
C) 21x⁸
D) 21x⁵³

Question 11

Which of the following values are closes to the roots of the following quadratic equation: ?

A) 0 and 4
B) 1 and 4
C) 0.5 and 3
D) 0.3 and 3.7

Question 12

is equal to:

A) 5y
B) y
C) y⁵
D) 5y⁵

Question 13

Another way of writing e^log(x) is:

A) 1
B) log(x)
C) e^x
D) x

Question 14

What are the roots of the equation y = 2x² + 2x - 4?

A) -2 and 1
B) -1 and 2
C) -2 and 2
D) -2 (repeated)

Question 15

A) B)
Which of the following statements is true about graph (A) above?

A) The intercept of the graph is positive and its slope is negative
B) The intercept of the graph is negative and its slope is positive
C) Both the intercept and slope of the graph are positive
D) It is impossible to say anything about the intercept and slope without seeing the mathematical equation

Question 16

"x to the power 3" could be written:

A) 3x
B) 3x³
C) x³
D) 3x * 3x * 3x

Question 17

What are the roots of the equation y = x² + 2x - 6 closest to?

A) -4 and 2
B) -3.65 and 1.65
C) -7.3 and 3.3
D) Both complex

Question 18

The rank of matrices A and B from the previous question are:

A) 1 and 2, respectively
B) 2 and 1, respectively
C) 1 and 3, respectively
D) 3 and 1, respectively

Question 19

Writing out all the terms in the expression would lead to:

A) x₁₁ + x₁₂ + x₂₁ + x₂₂
B) x₁₁ + x₁₂ +x₂₁ + x₂₂
C) x₁ + x₂
D) x₁₁ + x₂₂

Question 20

What is the (first order) derivative of the function ?

A)
B)
C)
D)

Question 21

For two conformable matrices A and B, expanding the parentheses of (AB)^-1 gives:

A) A^-1B^-1
B) B^-1A^-1
C) BA
D) AB

Question 22

The point where the capital market line is tangential to the efficient frontier is

A) The point where the portfolio returns are minimised
B) The point where the portfolio returns are maximised
C) The point where the portfolio's Sharpe ratio is minimised
D) The point where the portfolio's Sharpe ratio is maximised

Question 23

What is the inverse of matrix ?

A)
B)
C)
D)

Question 24

Consider the following two graphs:
A. B. Which of the following statements is true if A represents a normal distribution?
(I) The skewness of the distribution plot A is 0 and its kurtosis is 3
(II) The skewness of the distribution plot B is 0 and its kurtosis is 3
(III) The excess kurtosis of the distribution plot A is 3
(IV) The excess kurtosis of the distribution plot B is 0

A) Both (I) and (III) are true
B) Only (III) is true
C) Only (I) is true
D) Both (I) and (IV) are true

Question 25

The rank of a square matrix is also:

A) The product of the eigenvalues
B) The sum of the eigenvalues
C) The number of non-zero eigenvalues
D) The number of correlated rows or columns

Question 26

Consider the following data series: 11, 10, 6, 8, 4, 3, 7. What is its semi-interquartile range of this series?

A) 6
B) 5
C) 4
D) 3

Question 27

The central limit theorem states that

A) The sampling distribution of the mean of any random sample of observations will tend towards the normal distribution with mean equal to the population mean as the sample size tends to infinity
B) The sampling distribution of the mean of any random sample of observations will tend towards the normal distribution with mean equal to the population mean as the sample size tends to zero
C) The cumulative distribution function of the mean of any random sample of observations will tend towards the normal distribution with mean equal to the population mean as the sample size tends to infinity
D) The probability distribution function of the mean of any random sample of observations will tend towards the normal distribution with mean equal to the population mean as the sample size tends to infinity

Question 28

The trace of matrix C is

A) 9
B) 8
C) 7
D) 6