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Integrated Business FoundationBUS B200F
DM Module | Simple Linear Regression
Integrated Business FoundationBUS B200F
Module 9
Decision Making Skills
Simple Linear
Regression
Integrated Business FoundationBUS B200F
DM Module | Simple Linear Regression
Lecture Outline
Regression and Correlation
Least Squares Regression Equation
Regression in Excel
Regression Assumptions
Inferences about the Slope and Correlation Coefficients
Estimation of Mean Values and Prediction of Individual Values
Remarks for Regression
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Integrated Business FoundationBUS B200F
DM Module | Simple Linear Regression
What is Regression Analysis
Regression Analysis is used to
Predict the value of a Dependent Variable (Response, Y) based on the value of at
least one Independent Variable (Predictor, Xi)
Explain the impact of changes in Independent Variable (Predictor, Xi) an on the
Dependent Variable (Response, Y)
Simple Linear Regression
Only one independent variable, X
Relationship between X and Y is described by a linear function
Changes in the continuous variable Y are assumed to be related to changes in X
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Integrated Business FoundationBUS B200F
DM Module | Simple Linear Regression
Dependent and Independent Variables
Dependent variable: the variable we wish to predict or explain
Independent variable: the variable (or factor) used to explain the dependent
variable
Examples:
Dependent variable
Y
Independent variable
X
Exam score Test score
Sales of ice-cream Outdoor temperature
Project completion time Number of workers
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Integrated Business FoundationBUS B200F
DM Module | Simple Linear Regression
Check for Linear Relationship
To observe if there is any linear relationship between variables X and Y, we
need to take n pairs of observations, (x1,y1), …, (xn,yn), then either
Plot the data set into a scatter plot (of Y against X) to show the relationship between the
two variables
Perform a correlation analysis to measure the strength of the linear association between
the two variables
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YYnXXn
YXXYn
r
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Integrated Business FoundationBUS B200F
DM Module | Simple Linear Regression
Types of Relationships between Variables
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Integrated Business FoundationBUS B200F
DM Module | Simple Linear Regression
Types of Relationships between Variables
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Integrated Business FoundationBUS B200F
DM Module | Simple Linear Regression
Types of Relationships between Variables
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Integrated Business FoundationBUS B200F
DM Module | Simple Linear Regression
Correlation Coefficient (r )
Measures the strength of linear relationship of two variables
Sample correlation coefficient, r
where
and sX and sY are the sample standard deviation of X and Y respectively