R04 Introduction to Linear Regression 2020 Level II Notes
R04 Introduction to Linear Regression
1. Introduction...................................................................................................................................................................2
2. Linear Regression .......................................................................................................................................................2
2.1. Linear Regression with One Independent Variable ..........................................................................2
3. Assumptions of the Linear Regression Model...............................................................................................4
4. The Standard Error of Estimate ...........................................................................................................................5
5. The Coefficient of Determination ........................................................................................................................5
6. Hypothesis Testing .....................................................................................................................................................5
7. Analysis of Variance in a Regression with One Independent Variable .............................................7
8. Prediction Intervals ...................................................................................................................................................9
9. Limitations of Regression Analysis ................................................................................................................. 11
Summary ........................................................................................................................................................................... 12
This document should be read in conjunction with the corresponding reading in the 2020 Level II
CFA® Program curriculum. Some of the graphs, charts, tables, examples, and figures are copyright
2019, CFA Institute. Reproduced and republished with permission from CFA Institute. All rights
reserved.
Required disclaimer: CFA Institute does not endorse, promote, or warrant the accuracy or quality of
the products or services offered by IFT. CFA Institute, CFA®, and Chartered Financial Analyst® are
trademarks owned by CFA Institute.
© IFT. All rights reserved 1
, R04 Introduction to Linear Regression 2020 Level II Notes
1. Introduction
Financial analysts often need to predict whether one variable X can be used to predict
another variable Y. Linear regression allows us to examine this relationship. This reading
covers regression analysis with a single independent variable, X1. In the next reading we will
cover regression analysis with multiple independent variables, X 1, X2, X3….
2. Linear Regression
2.1. Linear Regression with One Independent Variable
Linear regression assumes a linear relationship between the dependent and independent
variables. Regression analysis uses the historical relationship between the independent
variable and the dependent variable to predict the values of the dependent variable. The
regression equation is expressed as follows:
Yi = b0 + bi Xi + εi
where:
i = 1, …, n
Y = dependent variable
b0 = intercept
b1 = slope coefficient
X = independent variable
ε = error term
b0 and b1 are called the regression coefficients.
Dependent variable is the variable being predicted. It is denoted by Y in the equation. The
variable used to explain changes in the dependent variable is the independent variable. It is
denoted by X. The equation shows how much Y changes when X changes by one unit.
Say that we want to estimate the regression relation between the annual rate of inflation
(the dependent variable) and annual rate of money supply growth (the independent
variable) for six industrialized countries. The following table shows the data from these
countries from 1980 to 2016.
Country Money Supply Growth Rate (%) Inflation Rate (%)
Australia 10.68 4.14
Japan 4.00 0.32
South Korea 16.65 4.86
Switzerland 5.54 1.67
United Kingdom 11.81 4.10
United States 6.28 2.77
Average 9.16 2.98
The figure below demonstrates how linear regression works. It shows a scatter plot
© IFT. All rights reserved 2
R04 Introduction to Linear Regression
1. Introduction...................................................................................................................................................................2
2. Linear Regression .......................................................................................................................................................2
2.1. Linear Regression with One Independent Variable ..........................................................................2
3. Assumptions of the Linear Regression Model...............................................................................................4
4. The Standard Error of Estimate ...........................................................................................................................5
5. The Coefficient of Determination ........................................................................................................................5
6. Hypothesis Testing .....................................................................................................................................................5
7. Analysis of Variance in a Regression with One Independent Variable .............................................7
8. Prediction Intervals ...................................................................................................................................................9
9. Limitations of Regression Analysis ................................................................................................................. 11
Summary ........................................................................................................................................................................... 12
This document should be read in conjunction with the corresponding reading in the 2020 Level II
CFA® Program curriculum. Some of the graphs, charts, tables, examples, and figures are copyright
2019, CFA Institute. Reproduced and republished with permission from CFA Institute. All rights
reserved.
Required disclaimer: CFA Institute does not endorse, promote, or warrant the accuracy or quality of
the products or services offered by IFT. CFA Institute, CFA®, and Chartered Financial Analyst® are
trademarks owned by CFA Institute.
© IFT. All rights reserved 1
, R04 Introduction to Linear Regression 2020 Level II Notes
1. Introduction
Financial analysts often need to predict whether one variable X can be used to predict
another variable Y. Linear regression allows us to examine this relationship. This reading
covers regression analysis with a single independent variable, X1. In the next reading we will
cover regression analysis with multiple independent variables, X 1, X2, X3….
2. Linear Regression
2.1. Linear Regression with One Independent Variable
Linear regression assumes a linear relationship between the dependent and independent
variables. Regression analysis uses the historical relationship between the independent
variable and the dependent variable to predict the values of the dependent variable. The
regression equation is expressed as follows:
Yi = b0 + bi Xi + εi
where:
i = 1, …, n
Y = dependent variable
b0 = intercept
b1 = slope coefficient
X = independent variable
ε = error term
b0 and b1 are called the regression coefficients.
Dependent variable is the variable being predicted. It is denoted by Y in the equation. The
variable used to explain changes in the dependent variable is the independent variable. It is
denoted by X. The equation shows how much Y changes when X changes by one unit.
Say that we want to estimate the regression relation between the annual rate of inflation
(the dependent variable) and annual rate of money supply growth (the independent
variable) for six industrialized countries. The following table shows the data from these
countries from 1980 to 2016.
Country Money Supply Growth Rate (%) Inflation Rate (%)
Australia 10.68 4.14
Japan 4.00 0.32
South Korea 16.65 4.86
Switzerland 5.54 1.67
United Kingdom 11.81 4.10
United States 6.28 2.77
Average 9.16 2.98
The figure below demonstrates how linear regression works. It shows a scatter plot
© IFT. All rights reserved 2
