The Significance of the Model Robb T Koether Homework Review Introduction The True Model Linear Regression Analysis Testing the Significance of the Relationship Testing the Significance on the TI 83 Significance vs Strength of the Relationship The Significance of the Model Lecture 47 Section 13 10 Robb T Koether Hampden Sydney College Tue Nov 24 2009 Outline The Significance of the Model 1 Homework Review 2 Introduction 3 The True Model The True Model 4 Linear Regression Analysis Linear Regression Analysis 5 Testing the Significance of the Relationship 6 Testing the Significance on the TI 83 7 Significance vs Strength of the Relationship 8 Assignment Robb T Koether Homework Review Introduction Testing the Significance of the Relationship Testing the Significance on the TI 83 Significance vs Strength of the Relationship Outline The Significance of the Model 1 Homework Review 2 Introduction 3 The True Model The True Model 4 Linear Regression Analysis Linear Regression Analysis 5 Testing the Significance of the Relationship 6 Testing the Significance on the TI 83 7 Significance vs Strength of the Relationship 8 Assignment Robb T Koether Homework Review Introduction Testing the Significance of the Relationship Testing the Significance on the TI 83 Significance vs Strength of the Relationship Homework Review The Significance of the Model Robb T Koether Homework Review Introduction The True Model Linear Regression Analysis Testing the Significance of the Relationship Testing the Significance on the TI 83 Significance vs Strength of the Relationship Practice Problem Date Jan 16 Jan 23 Jan 30 Feb 6 Feb 13 Feb 20 Feb 27 Mar 6 Mar 13 Mar 20 Mar 27 Apr 3 Crude Oil 40 98 41 05 42 07 41 77 43 04 39 87 40 22 42 85 42 91 44 90 50 10 48 09 Date Jan 19 Jan 26 Feb 2 Feb 9 Feb 16 Feb 23 Mar 2 Mar 9 Mar 16 Mar 23 Mar 30 Apr 9 Gasoline 1 833 1 833 1 894 1 926 1 970 1 924 1 942 1 936 1 921 1 950 2 048 2 044 Homework Review The Significance of the Model Robb T Koether Homework Review Introduction The True Model Linear Regression Analysis Testing the Significance of the Relationship Testing the Significance on the TI 83 Significance vs Strength of the Relationship Practice Problem a Draw the scatter plot b Find the equation of the regression line c Perform the residual analysis d Find the correlation coefficient e Find the coefficient of determination f Compute SST SSR and SSE Solution The Significance of the Model Robb T Koether Homework Review Practice Problem a The scatter plot 2 05 Introduction The True Model Linear Regression Analysis Testing the Significance of the Relationship Testing the Significance on the TI 83 Significance vs Strength of the Relationship 2 00 1 95 1 90 1 85 40 42 44 46 48 50 Solution The Significance of the Model Robb T Koether Homework Review Introduction The True Model Linear Regression Analysis Testing the Significance of the Relationship Testing the Significance on the TI 83 Significance vs Strength of the Relationship Practice Problem b Store oil prices in L1 and gas prices in L2 Enter LinReg a bx L1 L2 Y1 and press ENTER The equation of the regression line is y 1 189 0 01728x Solution The Significance of the Model Robb T Koether Homework Review Practice Problem c The residual plot 0 10 Introduction The True Model Linear Regression Analysis Testing the Significance of the Relationship Testing the Significance on the TI 83 Significance vs Strength of the Relationship 0 05 0 00 0 05 0 10 40 42 44 46 48 50 There is no curvature so a linear model is appropriate Solution The Significance of the Model Robb T Koether Homework Review Introduction The True Model Linear Regression Analysis Testing the Significance of the Relationship Testing the Significance on the TI 83 Significance vs Strength of the Relationship Practice Problem d When we did LinReg we saw that the correlation coefficient was r 0 8090 e The coefficient of determination is r2 0 6545 Solution The Significance of the Model Robb T Koether Homework Review Introduction Practice Problem e SST sum L2 y 2 0 0490 SSR R2 SST 0 0321 The True Model Linear Regression Analysis Testing the Significance of the Relationship Testing the Significance on the TI 83 Significance vs Strength of the Relationship Therefore SSE SST SSR 0 0490 0 0321 0 0169 Outline The Significance of the Model 1 Homework Review 2 Introduction 3 The True Model The True Model 4 Linear Regression Analysis Linear Regression Analysis 5 Testing the Significance of the Relationship 6 Testing the Significance on the TI 83 7 Significance vs Strength of the Relationship 8 Assignment Robb T Koether Homework Review Introduction Testing the Significance of the Relationship Testing the Significance on the TI 83 Significance vs Strength of the Relationship Introduction The Significance of the Model Robb T Koether Homework Review Introduction The True Model Linear Regression Analysis Testing the Significance of the Relationship Testing the Significance on the TI 83 Significance vs Strength of the Relationship We finally address the question of whether the relationship between x and y is significant If it is not significant then any correlation we observe is purely accidental This is relatively likely in small samples where randomness dominates In larger samples it is not likely but weak accidental correlations are still possible We will perform a test that will settle the question up to a level of certainty Introduction The Significance of the Model Robb T Koether Homework Review Introduction The True Model Linear Regression Analysis Testing the Significance of the Relationship Testing the Significance on the TI 83 Significance vs Strength of the Relationship We finally address the question of whether the relationship between x and y is significant If it is not significant then any correlation we observe is purely accidental This is relatively likely in small samples where randomness dominates In larger samples it is not likely but weak accidental correlations are still possible We will perform a test that will settle the question up to a level of certainty Introduction The Significance of the Model Robb T Koether Homework Review Introduction The True Model Linear Regression Analysis Testing the Significance of the Relationship Testing the Significance on the TI 83 Significance vs Strength of the Relationship We finally address the question of whether the relationship between x and y is significant If it is not significant then any correlation we observe is purely
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