tailieunhanh - Lecture Introductory Econometrics for Finance: Chapter 2 - Chris Brooks

Chapter 2 - Mathematical and statistical foundations. This chapter presents the following content: Straight lines, plot of hours studied against mark obtained, quadratic functions, the roots of quadratic functions, calculating the roots of quadratics, manipulating powers and their indices, logarithms, how do logs work?,.and other contents. | ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Chapter 2 Mathematical and Statistical Foundations Introductory Econometrics for Finance Copyright 2002, Chris Brooks ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Functions A function is a mapping or relationship between an input or set of inputs and an output We write that y, the output, is a function f of x, the input, or 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 a curve 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 Introductory Econometrics for Finance Copyright 2002, Chris Brooks ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Straight Lines The intercept is the point at which the line crosses the y-axis Example: . | ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Chapter 2 Mathematical and Statistical Foundations Introductory Econometrics for Finance Copyright 2002, Chris Brooks ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Functions A function is a mapping or relationship between an input or set of inputs and an output We write that y, the output, is a function f of x, the input, or 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 a curve 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 Introductory Econometrics for Finance Copyright 2002, Chris Brooks ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Straight Lines The intercept is the point at which the line crosses the y-axis Example: suppose that we were modelling 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 + The intercept, a, is 25 and the slope, b, is This means that with no study (x=0), the student could expect to earn a mark of 25% For every hour of study, the grade would on average improve by , so another 100 hours of study would lead to a 5% increase in the mark Introductory Econometrics for Finance Copyright 2002, Chris Brooks ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Plot of Hours Studied Against Mark Obtained Introductory Econometrics for Finance Copyright 2002, Chris Brooks ‘Introductory Econometrics for Finance’ © Chris Brooks 2013 Straight Lines In the graph above, the slope is positive . the line slopes upwards from left to right But in other examples the gradient could be zero or negative For a straight line the slope is .

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