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Chapter 16

# OMIS 2010 Chapter Notes - Chapter 16: Regression Analysis, Interval Estimation, Royal Guelphic Order

Department
Operations Management and Information System
Course Code
OMIS 2010
Professor
Alan Marshall
Chapter
16

This preview shows pages 1-2. to view the full 7 pages of the document. Chapter 16: Sample Linear Regression and Correlation
-Regression analysis: used to predict value of one variable on basis of other variables
-Dependent variable: variable to be forecast
-Independent variable: variable that practitioner believes are related to dependent variables (x1, x2, xk)
-Correlation analysis: determines whether relationship exists
Model
-Deterministic models: equation that allow us to determine value of the dependent variable from values of
independent variables
-Probabilistic Model: method to represent randomness
-e is the error variable: accounts for all variables, measurable and immeasurable, that are not part of the
model
oIts value varies from one ‘sale’ to the next even if ‘x’ remains constant
-First-Order Linear Model (simple linear regression model): y (dependent variable) = B0 (y-int) – (y-int)
B1x(independent variable) + e (error variable)
-X and y must be interval
Estimating the Coefficients
-Draw random samples from population of interest
-Calculate sample statistics to estimate B0 and B1
-Estimators based on drawing straight line though sample data; least squares line: comes closest to sample
data points
oY-hat (predicted/fitted value of y) = b0 +b1x
oB0 and b1 calculated so that sum of squared deviations is minimized
oY-hat on average comes closest to observed values of y
oLeast squares method: produces straight line that minimizes the sum of the squared difference
between the points and the line
o(b0) and (b1) are unbiased estimators of B0 and B1
oResiduals: deviations between the actual data pints and the line, ei
oEi = yi – y-hat
Residuals are observations of the error variable

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

Minimized sum of squared deviation called sum of squares for error (SSE)
Residuals are differences between observed values of y1 and y hat
-Note: we can’t determine value of y-hat for value of x that is far outside the range of sample values of x
Error Variable: Required Conditions
-Required conditions for the Error Variable
1. Probability distribution of e is normal
2. Mean of the distribution is 0: E€ = 0
3. Standard deviation of e is sigma e, which is constant regardless of value of x
4. Value of e associate with any particular value of y is independent of e associated with any
other value of y
-For 1, 2, 3: for each value of x, y is a normally distributed random variable with mean: E(y) = B0 + B1x, with
standard deviation of sigma-e
oMean depends on x, std deviation constant for all values of x
oFor each x, y is normally distributed with same standard deviation
Observational and Experimental Data
-Objective is to see how independent variable is related to dependent variable
-When data is observational, both variables are random variable (don’t need to specify which is
dependent and which is not)
-Two variables must be bivariate normally distributed
Assessing the Model
-Least squares method produces best straight line
oStill may not be any relationship or nonlinear relationship between the two variable’s
-Standard error of the estimate: t-test of the slope and coefficient of determination
Sum of Squares for Error
-Least squares method determines coefficient that minimize sum of squared deviations between the points
and the line defined by the coefficients
Standard Error of Estimate
-If sigma e is large, some of the errors will be large