dd8fasimple linear regression 1
TRANSCRIPT
-
8/14/2019 Dd8faSimple Linear Regression 1
1/11 1
Amity Business School
Simple Linear Regression Simple Linear Regression Model
Least Squares Method
Coefficient of Determination
Model Assumptions
Testing for Significance Using the Estimated Regression Equation
for Estimation and Prediction
Computer Solution
Residual Analysis: Validating Model Assumptions
-
8/14/2019 Dd8faSimple Linear Regression 1
2/112
Amity Business School
Introduction Sir Francis Galton F.R.S 1822 - 1911
http://images.google.com/imgres?imgurl=http://www.eugenicsarchive.org/images/eugenics/normal/951-1000/960-Sir-Francis-Galton.jpg&imgrefurl=http://www.eugenicsarchive.org/html/eugenics/static/images/960.html&usg=__l6RrvQZWpyC03NH6vKDsevr5bzQ=&h=772&w=568&sz=79&hl=en&start=16&um=1&tbnid=GgD2XG1mVb3VhM:&tbnh=142&tbnw=104&prev=/images%3Fq%3Dgalton%2Blaboratory%26hl%3Den%26rls%3Dcom.microsoft:en-US%26sa%3DN%26um%3D1 -
8/14/2019 Dd8faSimple Linear Regression 1
3/113
Amity Business School
Introduction Regression Analysis is used to predict
the value of one variable on the basis ofother variable.
The variable being predicted, is called thedependent variable.
The variable or variables being used topredict the value of dependent variable arecalled Independent Variable.
-
8/14/2019 Dd8faSimple Linear Regression 1
4/114
Amity Business School
Illustration The product manager in charge of ABC brand of
children's breakfast cereal would like to predict the
demand for cereal during the next year. To use
regression analysis he and his staff list the following
variables as likely to affect his sales:
1. Price of the product, 2.No of Children 5 to 12 years ofage, 3. Price of competitors products, 4.Effectiveness of
Advertising, 5.Annual sales this year, 6.Annual sales in
the previous year
-
8/14/2019 Dd8faSimple Linear Regression 1
5/115
Amity Business School
Simple Linear RegressionModel
y = b0 + b1x +e
where:
b0 and b1 are called parameters of the model,
e is a random variable called the error term.
The simple linear regression model is:
The equation that describes how y is related to x andan error term is called the regression model.
-
8/14/2019 Dd8faSimple Linear Regression 1
6/116
Amity Business School
Simple Linear Regression Equation
The simple linear regression equation is:
E(y) is the expected value of y for a given x value.
b1 is the slope of the regression line.
b0 is the y intercept of the regression line.
Graph of the regression equation is a straight line.
E(y) = b0 + b1x
-
8/14/2019 Dd8faSimple Linear Regression 1
7/117
Amity Business School
Positive Linear Relationship
E(y)
x
Slopeb1
is positive
Regression line
Interceptb
0
-
8/14/2019 Dd8faSimple Linear Regression 1
8/118
Amity Business School
Negative Linear Relationship
E(y)
x
Slopeb1is negative
Regression lineInterceptb0
-
8/14/2019 Dd8faSimple Linear Regression 1
9/119
Amity Business School
No Relationship
E(y)
x
Slopeb1
is 0
Regression lineIntercept
b0
-
8/14/2019 Dd8faSimple Linear Regression 1
10/1110
Amity Business School
Estimated Simple Linear Regression Equation
The estimated simple linear regression equation
0 1y b b x
is the estimated value of y for a given x value.y
b1 is the slope of the line.
b0 is the y intercept of the line.
The graph is called the estimated regression line.
-
8/14/2019 Dd8faSimple Linear Regression 1
11/1111
Amity Business School
Estimation ProcessRegression Model
y = b0 + b1x +eRegression Equation
E(y) = b0 + b1xUnknown Parameters
b0,b1
Sample Data:x y
x1 y1. .
. .
xn yn
b0 and b1provide estimates of
b0 and b1
EstimatedRegression Equation
Sample Statisticsb0, b1
0 1y b b x