Estatstica e Modelos Probabilsticos - COE241 Aula de hoje Introduo - - PowerPoint PPT Presentation
Estatstica e Modelos Probabilsticos - COE241 Aula de hoje Introduo a Regresso linear Rosa Leo 2018 Scatter Diagrams A scatter plot scatter plot is a graph that may be used to represent the 2 relationship between two
Rosa Leão – 2018
Aula de hoje Introdução a Regressão linear
Rosa Leão – 2018
X n−1
2
=n−1S
2
0
2
A scatter plot scatter plot is a graph that may be used to represent the relationship between two variables. Also referred to as a scatter scatter diagram diagram.
Rosa Leão – 2018
A dependent variable dependent variable is the variable to be predicted or explained in a regression model. This variable is assumed to be functionally related to the independent variable.
Rosa Leão – 2018
An independent variable independent variable is the variable related to the dependent variable in a regression equation. The independent variable is used in a regression model to estimate the value
Rosa Leão – 2018
X Y
(a) Linear (a) Linear
Rosa Leão – 2018
X Y
(b) Linear (b) Linear
Rosa Leão – 2018
X Y
(c) Curvilinear (c) Curvilinear
Rosa Leão – 2018
X Y
(d) Curvilinear (d) Curvilinear
Rosa Leão – 2018
X Y
(e) No (e) No Relationship Relationship
Rosa Leão – 2018
The correlation coefficient correlation coefficient is a quantitative measure of the strength
from + 1.0 to - 1.0. A correlation of 1.0 indicates a perfect linear relationship, whereas a correlation of 0 indicates no linear relationship.
Rosa Leão – 2018
CORRELATION COEFFICIENT CORRELATION COEFFICIENT
where:
r = correlation coefficient sx = standard deviation of X sy = standard deviation of Y
Rosa Leão – 2018
SAMPLE CORRELATION COEFFICIENT SAMPLE CORRELATION COEFFICIENT
where:
r = Sample correlation coefficient n = Sample size x = Value of the independent variable y = Value of the dependent variable
2 2
Rosa Leão – 2018
Simple linear regression analysis Simple linear regression analysis analyzes the linear relationship that exists between a dependent variable and a single independent variable.
Rosa Leão – 2018
SIMPLE LINEAR REGRESSION MODEL SIMPLE LINEAR REGRESSION MODEL
where: y = Value of the dependent variable x = Value of the independent variable a = Population’s y-intercept b = Slope of the population regression line = Error term, or residual
ε
Rosa Leão – 2018
REGRESSION COEFFICIENTS REGRESSION COEFFICIENTS In the simple regression model, there are two coefficients: the intercept and the slope.
Rosa Leão – 2018
The interpretation of the regression regression slope coefficient slope coefficient is that it gives the average change in the dependent variable for a unit increase in the independent variable. The slope coefficient may be positive or negative, depending on the relationship between the two variables.
Rosa Leão – 2018
The least squares criterion least squares criterion is used for determining a regression line that minimizes the sum of squared residuals.
i=1 n
( yi−(a+bxi))
2
estimated values Find a and b to minimize the sum bellow:
Rosa Leão – 2018
A residual
residual is the difference between the actual value of the dependent variable and the value predicted by the regression model.
Rosa Leão – 2018
X Y
4
300 20 100 400
^ y=150+60 x
Years with Company Sales in Thousands 390 390 312 312
Residual = 312 - 390 = -78
Rosa Leão – 2018