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Lecture 11

POL222H1 Lecture 11: How to Interpret Linear Regression Results
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Department
Political Science
Course Code
POL222H1
Professor
Kenichi Ariga

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POL222 – Lecture 12 How to interpret Linear Regression Results • How to interpret coefficient • Y = a+BX • B represents how much Y changes, on average, as X changes by one unit • You need to specify a particular unit used for X and Y when you substantively interpret B • Example: Economic voting in US Pres. Elections o Vote = 49.30 +0.75 x Growth o Should may attention to the unit measurement between independent and dependent variable because we need to use it for coefficient o As GDP growth rate improves by 1% point, the incumbent president’s party would gain 0.75 o Depends on unit of dependent variable, so 0.75 represented by vote share • Interpretation could be different depending on the unit of measurement • Question of substantive significance o Is the magnitude substantively large? ▪ We’d like to know if it is politically, economically, or socially important/meaningful o It may not necessarily be clear from the coefficient on X alone o Vote = 49.30 + 0.75 x Growth ▪ It isn’t clear if 0.75 is meaningful ▪ We need a measure • Whether the magnitude of the relationship found between Y and X is substantively large • Whether the magnitude of the relationship politically, economically, or socially important • There is no uniformly accepted term to call this concept • When you interpret or report the linear regression results, you should consider whether the relationship found is substantively significant • However, you need to make an argument whether or not the relationship found is substantively significant • How can we evaluate? • There is no uniform method to evaluate substantive significance • Hence you need to make an argument based on the linear regression results o Your creativity, logical and sensible reasoning, and convincing argumentation are called for o Given the causal theory • Argument based on the coefficient o Sometimes the substantive significance of the relationship may be immediate clear from the coefficient of X—Then you may make an argument based on the coefficient • Political scientist has been interested in the subject because there is a provision of government but that government would not be engage in important political decisions • The upset of the government would be a problem • So what determines the bargaining? • We have not seen the coalition government but in many countries coalition is known and in some governments the duration of bargaining was very long • In many cases substantive significant is not immediately clear • Example 2: standardized coefficient o Compute the change in Y we would expect on average corresponding to a typical change in X observed in data o Compare this expected amount of change in Y to a typical change in Y observed in data o We are going to use a certain typical change to evaluate substantive significance • Standard deviation As typical change o We use standard deviation to represent a typical change in Y and X observed in data o Standard deviation is the measure of variability of a variable • We can see a typical change in variable is much longer in Iran than in Canada • First we would compute the expected change in Y on average corresponding to typical change in Y measured by its standard deviation of the independent variable o B x sd (X) • Then compare this change in Y to a typical change in Y, measured by standard deviation (=sd (Y)) • Application: o Economic voting in the US presidential elections o Y = 49.30 + 0.75 x X • Step 1: compute the change of Y corresponding to a typical change in X, measured by its standard deviation o Standard deviation of the GDP growth rate is 4.32 o B x sd (X) = 0.65 x 4.32 = 3.24 • This number means: one standard deviation change in GDP growth rate would increase vote share by 3.24 • Step 2: compare this change in Y to a typical change in Y measured by its standard deviation o We divided the dependent variable by its standard deviation o Standardized coefficient = B x sd (X)/sd (Y) = 3.24/5.44 =
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