Problem 1. The following data is taken from Greenberg H., \"An Analysis of Traff

Question

Problem 1. The following data is taken from Greenberg H., "An Analysis of Traffic Flow," Operation Research 7, 79-85 (1959) Lincoln Tunnel Merritt Parkwa Velocity (m.p.h) 38.8 31.5 10.6 16.1 Velocity (m.p.h) 32 28 25 23 20 19 17 16 15 14 13 12 Density (cars/mile) 34 Density (cars/mile) 20.4 27.4 106.2 80.4 141.3 130.9 121.7 106.5 130.5 101.1 123.9 144.2 29.5 30.8 26.5 35.7 30.0 53 60 74 82 94 94 96 103 112 108 129 132 139 160 8.3 8.5 11.1 8.6 11.1 9.8 7.8 31.8 31.6 34.0 28.9 28.8 10 a) b) c) d) Use linear regression for the Lincoln Tunnel data for speed as a function of density Use quadratic regression for the Lincoln Tunnel data for flow as function of density Use exponential regression for Merritt Parkway data for speed as function of density For all the above three calculations, find square of correlation coefficient (R2)

Explanation / Answer

Regression Models :

Dependent variable = Y = Velocity

Independent variable ( Predictor variable ) = X = Density

Linear Regression Model :

Velocity = b0 + b1 * Density +error

lm(formula = Velocity ~ Density)

Coefficients:   

(Intercept) = b0 = 35.55098

Density = b1 = -0.20310

Multiple R-squared: 0.9435, Adjusted R-squared: 0.9398

Exponential Regression Model :  

Code for this :

Reg2 = nls(Velocity ~ (Density ^ b), start = c(b = -0.2031), trace = T)
summary(Reg2)
coef(Reg2)

then coefficient of this : b = 0.5768257

Qudratic Regression Model :

Velocity = b0 + b1 * Density + b2 * Density^2 +error

lm(formula = Velocity ~ Density + Density^2)

Coefficients:

(Intercept) = 38.38337   

Density = -0.23613   

Multiple R-squared: 0.9557, Adjusted R-squared: 0.9527

>>>>>>>>>>>> Best Luck >>>>>>>>>>>>>>>>>>

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