Unit 6 - Statistics V3100018.001-V3100018.006 UNIT 6...

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Statistics – V3100018.001-V3100018.006 UNIT 6 – Bivariate analytical tools: regression Giuseppe Arbia , Catholic University of the Sacred Hearth, Roma, Italy 1
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2 The correlation coefficient indicates the presence of a certain degree of linear dependence (that is a dependence along a straight line) between two quantitative variables With no distinction between the variable that is at the origin (the “cause”) and the variable that is the response (the “effect”).
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3 Linear relationship
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4 Non-linear relationship (quadratic)
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To study the relationships between pairs of quantitative variables we also use the idea of regression 5
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In regression analysis we distinguish the role of the two variables involved The Independent variable: is the variable that “ideally” is at the origin of the phenomenon (the “ cause”) The dependent variable is the response variable (The “effect”) 6 We do this through a statistical model
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What is a model ? E. g.: A model of Ferrari 7
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8 What is a statistical model A simplified representation of reality that reproduces some essential features while neglecting others. It is a stylized version of reality.
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9 Digression: a line Slope = β 1 Intercept = β 0 Y= β 0+ β 1 x
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Parameters of a line Y= β 0+ β 1 x : INTERCEPT β 0 represents the value of Y when X = 0. SLOPE β 1 represents the variation of Y when X increases of 1 unit. 10
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11 a b β 0 β 1 X=0 A numerical example
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12 Case of β 1 = 0 Y= β 0 β 0
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13 Case of β 1 > 0 Y= β 0+ β 1 x β 1 > 0
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14 Case of β 1 < 0 Y= β 0+ β 1 x β 1 < 0
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15 Case of β 1 = 1 (45 ° line) Y= β 0 +x Y=x
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16 Case of β 0 < 0 β 0
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17 Given a certain scatter diagram, among the many possible choices, how do we choose the best interplating line?
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