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picture1_Linear Regression Ppt 68971 | Chapter 13 Linear Regression


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File: Linear Regression Ppt 68971 | Chapter 13 Linear Regression
regression analysis our objective is to analyze the relationship between interval variables regression analysis is used to predict the value of one variable the dependent variable on the basis of ...

icon picture PPTX Filetype Power Point PPTX | Posted on 29 Aug 2022 | 3 years ago
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             Regression Analysis…
    • Our objective is to analyze the relationship 
      between interval variables; 
    • Regression analysis is used to predict the value 
      of one variable (the dependent variable) on 
      the basis of other variables (the independent 
      variables).
    • Dependent variable: denoted Y
    • Independent variables: denoted X , X , …, X
                                           1   2     k
    08/29/2022           Towson University - J. Jung    2
             Regression Analysis…
   • If we are interested only in determining whether 
     a relationship exists, we may employ correlation 
     analysis.
   • Regression analysis with two-variables is 
     sometimes called simple linear regression.
   • Mathematical equations describing their 
     relationships are also called models
   • 2 types: deterministic or probabilistic. 
    08/29/2022           Towson University - J. Jung    3
                  Model Types…
    • Deterministic Model: an equation or set of 
      equations that allow us to fully determine the 
      value of the dependent variable from the values 
      of the independent variables.
    • Contrast this with…
    • Probabilistic Model: a method used to capture 
      the randomness that is part of a real-life process.
    • E.g. do all houses of the same size (measured in 
      square feet) sell for exactly the same price?
    08/29/2022            Towson University - J. Jung    4
                         A Model…
     • To create a probabilistic model, we start with a 
       deterministic model that approximates the 
       relationship we want to model and add a random 
       term that measures the error of the deterministic 
       component.
     • Deterministic Model:
        –The cost of building a new house is about $75 per square 
          foot and most lots sell for about $25,000.
        –Hence the approximate selling price (y) would be: 
                                         2
          y = $25,000 + (75$/ft ) * x
        –(where x is the size of the house in square feet)
     08/29/2022                Towson University - J. Jung            5
                          A Model…
     • A model of the relationship between house size 
       (independent variable) and house price 
       (dependent variable) would be: 
                 House
                                                       
                  Price:                            ut
                                                  bo
                                                 a
                    Y                          s 
                                             st           ze
                                           co           Si
                                         e             * 
                                        s     .
                                      u     ot      5
                                     o             7
                                    h      o       
                                           f     +
                                  a     e      0
                                g       r     0
                               n      a     0
                             di      u     5
                            l       q
                            i      s      2
                         Bu     er      = 
                               p    ce
                             5     ri
       Most lots sell     $7    e P
                            ous
       for $25,000         H
                                                     House size: X
 In this model, the price of the house is completely determined by the size.
     08/29/2022                  Towson University - J. Jung              6
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