plz solve question (b) with explanation within 30-40 mins and get upvotes. crash329201263170AADTQuestion 3 (The records of crash frequency and annual average daily traffic volume (AADT) in 2009-2012were collected from 48 roadway segments of Highway 401 between Windsor and London inOntario. The data are stored in data-2009-2012.txt posted on Blackboard. A crash frequencymodel was developed to predict the number of crashes based on AADT using a linear regressionmodel as follows:103600107300107300107500971001256007190053000460004360047916025787651325832537064y = -13.1 + 0.002 * x4570045700599006840066600where y = crash frequency (“crash" in the file) and x = AADT.(a) Plot the graphs of the observed crash frequencies (x-axis) and the predicted crash frequenciesusing the above linear regression model (y-axis) in a scatter chart. Calculate the value of Rusing the following equations:1035263100474765700634006570083546610069700R² =1- SSESST687168100696009664205085796650055700where SSE = the sum of squares of errors (or the unexplained variance by the model), SST =the total variance in the data, y,= observed crash frequency for segment i; ŷ,= the predicted2700026700crash frequency for segment i; ỹ= average observed crash frequency for all segments; and n= number of segments (= 48).26400240002240011(b) Calculate the t-statistics of the coefficient of AADT (b = 0.002) using the following equation:38492310021300421721300218002340021500SSE/(n – 2)E:(xi – x)²5373where x = observed AADT for segment i; x = average observed AADT for all segments.70853666181001930021000Assess statistical significance of the coefficient b at a 95% confidence interval usinghypothetical testing. Assume null hypothesis (Ho): b is not statistically different from zero andalternative hypothesis (H1): b is statistically different from zero. Sketch a t-distribution curveand show 1) the calculated t-statistics; 2) the critical values of t-statistics (tenit,0.025 = 2.01 forsample size = 48); and 3) the confidence interval in the sketch.219003124172090024000224002220020200173001210064504425187(c) Based on the sign of the coefficient b, discuss the effect of AADT on crash frequency. Is theeffect realistic? Explain.1

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Answered: (b) Calculate the t-statistics of the…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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