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الدراسات والتعليم الجامعي / Regression Analysis
« في: أبريل 27, 2008, 01:52:44 مساءاً »
تحليل الانحدار من الموضوعات المهمة للاحصائيين
وهذا نبذه عن هذا المجال
Definition: Regression Analysis is a statistical
method for investigating functional
relationships among variables.
Examples:
• Height of son (Y) Height of father (X)
• Travel time (Y), Distance traveled (X1),
and Speed (X2)
Goals of Regression Analysis
To build an equation that allows us to
describe, predict, and control a dependent
(response) variable on the basis of one or
more predictor (explanatory) variables, that
is, to:
• Provide a good description of the behavior
of the response variable
• Predict future responses
• Extrapolate (predict responses outside the
range of the data)
• Estimate parameters (coefficients)
• Control the response variable by varying
levels of input (explanatory) variables
• Develop realistic models of the process
Regression Inputs
1. The Data:
n observations (cases) on a response Y
and p predictor variables X1, X2, …, Xp
2. The Regression Model:
yi = β 0 + β1 xi1 + β 2 xi2 + ... + β p xip +ε i
i =1,2,...,n
Y = Xβ + ε
3. The Method of Estimation (Fitting):
A common method for the estimation of the
regression parameters β is least squares.
Least Squares (LS):
وانشاء الله البقيه ستأتى
وهذا نبذه عن هذا المجال
Definition: Regression Analysis is a statistical
method for investigating functional
relationships among variables.
Examples:
• Height of son (Y) Height of father (X)
• Travel time (Y), Distance traveled (X1),
and Speed (X2)
Goals of Regression Analysis
To build an equation that allows us to
describe, predict, and control a dependent
(response) variable on the basis of one or
more predictor (explanatory) variables, that
is, to:
• Provide a good description of the behavior
of the response variable
• Predict future responses
• Extrapolate (predict responses outside the
range of the data)
• Estimate parameters (coefficients)
• Control the response variable by varying
levels of input (explanatory) variables
• Develop realistic models of the process
Regression Inputs
1. The Data:
n observations (cases) on a response Y
and p predictor variables X1, X2, …, Xp
2. The Regression Model:
yi = β 0 + β1 xi1 + β 2 xi2 + ... + β p xip +ε i
i =1,2,...,n
Y = Xβ + ε
3. The Method of Estimation (Fitting):
A common method for the estimation of the
regression parameters β is least squares.
Least Squares (LS):
وانشاء الله البقيه ستأتى