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Regression Analysis. Gordon Stringer . Regression Analysis. Regression Analysis: the study of the relationship between variables Regression Analysis: one of the most commonly used tools for business analysis Easy to use and applies to many situations. Regression Analysis.

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regression analysis

Regression Analysis

Gordon Stringer

Gordon Stringer, UCCS

regression analysis1
Regression Analysis
  • Regression Analysis: the study of the relationship between variables
  • Regression Analysis: one of the most commonly used tools for business analysis
  • Easy to use and applies to many situations

Gordon Stringer, UCCS

regression analysis2
Regression Analysis
  • Simple Regression: single explanatory variable
  • Multiple Regression: includes any number of explanatory variables.

Gordon Stringer, UCCS

regression analysis3
Regression Analysis
  • Dependant variable: the single variable being explained/ predicted by the regression model (response variable)
  • Independent variable: The explanatory variable(s) used to predict the dependant variable. (predictor variable)

Gordon Stringer, UCCS

regression analysis4
Regression Analysis
  • Linear Regression: straight-line relationship

Form: y=mx+b

  • Non-linear: implies curved relationships, for example logarithmic relationships

Gordon Stringer, UCCS

data types
Data Types
  • Cross Sectional: data gathered from the same time period
  • Time Series: Involves data observed over equally spaced points in time.

Gordon Stringer, UCCS

graphing relationships
Graphing Relationships
  • Highlight your data, use chart wizard, choose XY (Scatter) to make a scatter plot

Gordon Stringer, UCCS

scatter plot and trend line
Scatter Plot and Trend line
  • Click on a data point and add a trend line

Gordon Stringer, UCCS

scatter plot and trend line1
Scatter Plot and Trend line
  • Now you can see if there is a relationship between the variables. TREND uses the least squares method.

Gordon Stringer, UCCS

correlation
Correlation
  • CORREL will calculate the correlation between the variables
  • =CORREL(array x, array y)

or…

  • Tools>Data Analysis>Correlation

Gordon Stringer, UCCS

correlation1
Correlation
  • Correlation describes the strength of a linear relationship
  • It is described as between –1 and +1
  • -1 strongest negative
  • +1 strongest positive
  • 0= no apparent relationship exists

Gordon Stringer, UCCS

simple regression model
Simple Regression Model
  • Best fit using least squares method
  • Can use to explain or forecast

Gordon Stringer, UCCS

simple regression model1
Simple Regression Model
  • y = a + bx + e (Note: y = mx + b)
  • Coefficients: a and b
  • Variable a is the y intercept
  • Variable b is the slope of the line

Gordon Stringer, UCCS

simple regression model2
Simple Regression Model
  • Precision: accepted measure of accuracy is mean squared error
  • Average squared difference of actual and forecast

Gordon Stringer, UCCS

simple regression model3
Simple Regression Model
  • Average squared difference of actual and forecast
  • Squaring makes difference positive, and severity of large errors is emphasized

Gordon Stringer, UCCS

simple regression model4
Simple Regression Model
  • Error (residual) is difference of actual data point and the forecasted value of dependant variable y given the explanatory variable x.

Error

Gordon Stringer, UCCS

simple regression model5
Simple Regression Model
  • Run the regression tool.
  • Tools>Data Analysis>Regression

Gordon Stringer, UCCS

simple regression model6
Simple Regression Model
  • Enter the variable data

Gordon Stringer, UCCS

simple regression model7
Simple Regression Model
  • Enter the variable data
  • y is dependent, x is independent

Gordon Stringer, UCCS

simple regression model8
Simple Regression Model
  • Check labels, if including column labels
  • Check Residuals, Confidence levels to displayed them in the output

Gordon Stringer, UCCS

simple regression model9
Simple Regression Model
  • The SUMMARY OUTPUT is displayed below

Gordon Stringer, UCCS

simple regression model10
Simple Regression Model
  • Multiple R is the correlation coefficient
  • =CORREL

Gordon Stringer, UCCS

simple regression model11
Simple Regression Model
  • R Square: Coefficient of Determination
  • =RSQ
  • Goodness of fit, or percentage of variation explained by the model

Gordon Stringer, UCCS

simple regression model12
Simple Regression Model
  • Adjusted R Square =

1- (Standard Error of Estimate)2 /(Standard Dev Y)2

Adjusts “R Square” downward to account for the number of independent variables used in the model.

Gordon Stringer, UCCS

simple regression model13
Simple Regression Model
  • Standard Error of the Estimate
  • Defines the uncertainty in estimating y with the regression model
  • =STEYX

Gordon Stringer, UCCS

simple regression model14
Simple Regression Model
  • Coefficients:
    • Slope
    • Standard Error
    • t-Stat, P-value

Gordon Stringer, UCCS

simple regression model15
Simple Regression Model
  • Coefficients:
    • Slope = 63.11
    • Standard Error = 15.94
    • t-Stat = 63.11/15.94 = 3.96; P-value = .0005

Gordon Stringer, UCCS

simple regression model16
Simple Regression Model
  • y = mx + b
  • Y= a + bX + e
  • Ŷ = 56,104 + 63.11(Sq ft) + e
  • If X = 2,500 Square feet, then
  • $213,879 = 56,104 + 63.11(2,500)

Gordon Stringer, UCCS

simple regression model17
Simple Regression Model
  • Linearity
  • Independence
  • Homoscedasity
  • Normality

Gordon Stringer, UCCS

simple regression model18
Simple Regression Model
  • Linearity

Gordon Stringer, UCCS

simple regression model19
Simple Regression Model
  • Linearity

Gordon Stringer, UCCS

simple regression model20
Simple Regression Model
  • Independence:
    • Errors must not correlate
    • Trials must be independent

Gordon Stringer, UCCS

simple regression model21
Simple Regression Model
  • Homoscedasticity:
    • Constant variance
    • Scatter of errors does not change from trial to trial
    • Leads to misspecification of the uncertainty in the model, specifically with a forecast
    • Possible to underestimate the uncertainty
    • Try square root, logarithm, or reciprocal of y

Gordon Stringer, UCCS

simple regression model22
Simple Regression Model
  • Normality:
      • Errors should be normally distributed
      • Plot histogram of residuals

Gordon Stringer, UCCS

multiple regression model
Multiple Regression Model
  • Y = α + β1X1 + … + βkXk + ε
  • Bendrix Case

Gordon Stringer, UCCS

regression modeling philosophy
Regression Modeling Philosophy
  • Nature of the relationships
  • Model Building Procedure
    • Determine dependent variable (y)
    • Determine potential independent variable (x)
    • Collect relevant data
    • Hypothesize the model form
    • Fitting the model
    • Diagnostic check: test for significance

Gordon Stringer, UCCS