A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized. ŷ = bo + bịz +bzz? where y = traffic flow in vehicles per hour T= vehicle speed in miles per hour The following data were collected during rush hour for six highways leading out of the city. Traffic Flow (y) Vehicle Speed (2) 1256 36 1329 45 1226 30 1335 45 1349 55 1125 25 a. Use the data to compute the coefficients of this estimated regression equation (to 4 decimals). Enter negative value as negative number. (Create the z variable first using Data/Transform Data/Square.) bo = by = by = b. Using a = 0.01, test for a significant relationship. F = (to 4 decimals) p-value = (to 4 decimals) The relationship - Select your answer - significant. c. Estimate the traffic flow in vehicles per hour at a speed of 38 miles per hour (to 2 decimals). vehicles per hour

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized. ŷ = bo + bịz +bzz? where y = traffic flow in vehicles per hour T= vehicle speed in miles per hour The following data were collected during rush hour for six highways leading out of the city. Traffic Flow (y) Vehicle Speed (2) 1256 36 1329 45 1226 30 1335 45 1349 55 1125 25 a. Use the data to compute the coefficients of this estimated regression equation (to 4 decimals). Enter negative value as negative number. (Create the z variable first using Data/Transform Data/Square.) bo = by = by = b. Using a = 0.01, test for a significant relationship. F = (to 4 decimals) p-value = (to 4 decimals) The relationship - Select your answer - significant. c. Estimate the traffic flow in vehicles per hour at a speed of 38 miles per hour (to 2 decimals). vehicles per hour

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Description: 2 A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized.ŷ = bo + bịz + bzz?wherey = traffic flow in vehicles per hourT = vehicle speed in miles per hourThe following data were coll

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 32EQ

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A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = ?0 + ?1x + ? where y = traffic flow in vehicles per hour x = vehicle speed in miles per hour. The following data were collected during rush hour for six highways leading out of the city. Traffic Flow(y) Vehicle Speed(x) 1,254 35 1,330 40 1,228 30 1,334 45 1,351 50 1,126 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ = b0 + b1x + b2x2 (a) Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2. (Round b0 to the nearest integer and b1 to two decimal places and b2 to three decimal places.) ŷ = (b) Use ? = 0.01 to test for a significant relationship. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = (c)…
A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = ?0 + ?1x + ? where y = traffic flow in vehicles per hour x = vehicle speed in miles per hour. The following data were collected during rush hour for six highways leading out of the city. Traffic Flow(y) Vehicle Speed(x) 1,254 35 1,330 40 1,228 30 1,334 45 1,351 50 1,126 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ = b0 + b1x + b2x2 (a) Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2. (Round b0 to the nearest integer and b1 to two decimal places and b2 to three decimal places.) ŷ = (b) Use ? = 0.01 to test for a significant relationship. State the null and alternative hypotheses. H0: b0 = b1 = b2 = 0Ha: One or more of the parameters is not equal to zero.H0: One or more of the parameters is…
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