WorksheetsQuantitative Methods in Finance Quiz 3
Total questions: 20
Worksheet time: 10mins
What is the formal definition of a hypothesis according to the lecture?
A proven mathematical fact
A relationship between two or more phenomena
The final result of a regression analysis
A collection of random data points
Which of the following is considered a source for forming a hypothesis?
Media speculation
Only formal laboratory experiments
Software output from R only
Intercepts and slope coefficients
Which of the following is the BEST example of a structured hypothesis?
"How do culture and attitudes interact?"
"How do GDP and inflation affect each other?"
"Does education increase a person’s earnings?"
"Why are wages different across the country?"
When evaluating multiple hypotheses, what is an important question to ask?
Are the hypotheses mutually exclusive?
Can they be calculated without using a calculator?
Is the intercept always zero?
Are the variables only measured in currency?
In statistical testing, what does "rejecting a Null hypothesis" imply?
You must gather more data
You accept an alternative hypothesis
The regression line is incorrect
The correlation is zero
What is the primary function of regression analysis?
To prove that hypotheses are always true
To calculate a "line of best fit" between variables
To eliminate all errors in a data set
To summarize the mean and median of a single variable
What does Ordinary Least Squares (OLS) regression aim to minimize?
The number of variables in the equation
The sum of squared values of the vertical distances (errors)
The intercept value
The value of the slope coefficient
In the simple regression formula y = α 0 + β 1 * x + ϵ , what does "a" (or α 0) represent?
The slope coefficient
The error term
The intercept
The independent variable
What does the slope coefficient "b" (or β 1) predict?
The starting value of y when x is zero
How much y changes when x increases by 1 unit
The total sum of all observations
The relationship between more than three variables
In the example of wages and education, if y is wages and x is education, what are we trying to work out?
The average age of the participants
How much wages go up with each year of education
The total number of people in school
If culture affects education
Which mathematical rule is used to solve for coefficients a and b during derivation?
The addition rule
The chain rule
The division rule
The logic rule
According to the derived formula for a (intercept), how is it calculated?
a = y - b x
a = y + b x
a = b x / y
a = ϵ + y
When an observation is above the regression line, the vertical distance is considered:
Zero
Negative
Positive
Squared
What is the purpose of multiple regression compared to simple regression?
It only uses one independent variable
It calculates the mean of many datasets
It allows for the use of multiple independent variables (x1, x2, x3...)
It removes the intercept from the equation
What is a key strength of using multiple regression?
It makes the math simpler to do by hand
It holds other independent variables constant while estimating the effect of one
It ensures the correlation is always positive
It only works for financial data
In the multiple regression formula, what is $\beta$ (beta)?
A single number representing the average
A vector containing a full set of coefficients
The error term for the whole sample
The dependent variable
Which matrix formula is used to calculate the OLS coefficient vector in multiple regression?
β = (X'X)-1X'y
β = (Y'Y)X
y = α + β
a = y - bx
If you are holding "parental income" constant to see the effect of "education" on "wages," which method are you using?
Simple regression
Univariate statistics
Multiple regression
Null hypothesis rejection
When running a regression in a software package like R, what is reported?
Only the hypothesis
Coefficient values and other statistics
Just the line of best fit image
The chain rule derivation steps
What is the goal of the equation ∑ (yi - a - bxi)2?
To find the maximum error possible
To calculate the median
To identify the values that the regression tries to minimize
To define the alternative hypothesis
