Introductory Econometrics
Module Code: EF5154J
Academic Year:2023/2024
Lecturer: Dr. Marjan Zhaf
Lecture (1): Basic Mathematical Concepts
, Functions
A function is a mapping or relationship between an input or set of inputs and an
We write y = f(x)
y could be a linear function of x where the relationship can be expressed on a
straight line Or it could be non-linear where it would be expressed graphically as
If the equation is linear, we would write the relationship as
y = a + bx
where y and x are called variables and a and b are parameters
a is the intercept and b is the slope or gradient
, Straight Lines
The intercept is the point at which the line crosses the y-axis
Example: suppose that we were modeling the relationship between a student’s
average mark, y (in percent), and the number of hours studied per year, x
Suppose that the relationship can be written as a linear function
y = 25 + 0.05x
The intercept, a, is 25 and the slope, b, is 0.05
This means that with no study (x=0), the student could expect to earn a
mark of 25%. or every hour of study, the grade would on average improve by
0.05%, so another 100 hours of study would lead to a 5% increase in the mark
, Plot of Hours Studies Against Mark Obtained
Module Code: EF5154J
Academic Year:2023/2024
Lecturer: Dr. Marjan Zhaf
Lecture (1): Basic Mathematical Concepts
, Functions
A function is a mapping or relationship between an input or set of inputs and an
We write y = f(x)
y could be a linear function of x where the relationship can be expressed on a
straight line Or it could be non-linear where it would be expressed graphically as
If the equation is linear, we would write the relationship as
y = a + bx
where y and x are called variables and a and b are parameters
a is the intercept and b is the slope or gradient
, Straight Lines
The intercept is the point at which the line crosses the y-axis
Example: suppose that we were modeling the relationship between a student’s
average mark, y (in percent), and the number of hours studied per year, x
Suppose that the relationship can be written as a linear function
y = 25 + 0.05x
The intercept, a, is 25 and the slope, b, is 0.05
This means that with no study (x=0), the student could expect to earn a
mark of 25%. or every hour of study, the grade would on average improve by
0.05%, so another 100 hours of study would lead to a 5% increase in the mark
, Plot of Hours Studies Against Mark Obtained
