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A statistical program is recommended. A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y- Bo + Pax + 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 Vehicle Speed (x) (v) 1,258 35 1,329 40 1,224 30 1,336 45 1,351 50 1,124 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. (a) Develop an estimated regression equation for the data of the form- bo + b,x + b,x2. (Round b, to the nearest integer and b, to two decimal places and b, to three decimal places.) (b) Use a - 0.01 to test for a significant relationship. State the null and alternative hypotheses. O Hoi bo - b, - b, -0 H: One or more of the parameters is not equal to zero. O Ho: b, - b2 - 0 H: One or more of the parameters is not equal to zero. O Ho: One or more of the parameters is not equal to zero. O Ho: One or more of the parameters is not equal to zero. Hi bo- b - b2 -0

A statistical program is recommended. A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y- Bo + Pax + 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 Vehicle Speed (x) (v) 1,258 35 1,329 40 1,224 30 1,336 45 1,351 50 1,124 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. (a) Develop an estimated regression equation for the data of the form- bo + b,x + b,x2. (Round b, to the nearest integer and b, to two decimal places and b, to three decimal places.) (b) Use a - 0.01 to test for a significant relationship. State the null and alternative hypotheses. O Hoi bo - b, - b, -0 H: One or more of the parameters is not equal to zero. O Ho: b, - b2 - 0 H: One or more of the parameters is not equal to zero. O Ho: One or more of the parameters is not equal to zero. O Ho: One or more of the parameters is not equal to zero. Hi bo- b - b2 -0

Linear Algebra: A Modern Introduction
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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A statistical program is recommended. A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = Bo + B,x + 8 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) 1,258 35 1,329 40 1,224 30 1,336 45 1,351 50 1,124 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression eguation. ý = b, + b,x + b,x² (a) Develop an estimated regression equation for the data of the form ý = b, + b,x + b,x2. (Round b, to the nearest integer and b, to two decimal places and b, to three decimal places.) ý = (b) Use a = 0.01 to test for a significant relationship. State the null and alternative hypotheses. 0 = 29 = 'q - °g :°H O H.: One or more of the parameters is not equal to zero. O Ho: bị = b2 = 0 H: One or more of the parameters is not equal to zero. O H: One or more of the parameters is not equal to zero. H: b, = b2 = 0 O Ho: One or more of the parameters is not equal to zero. H: bo = b, = b2 = 0
Transcribed Image Text:A statistical program is recommended. A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = Bo + B,x + 8 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) 1,258 35 1,329 40 1,224 30 1,336 45 1,351 50 1,124 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression eguation. ý = b, + b,x + b,x² (a) Develop an estimated regression equation for the data of the form ý = b, + b,x + b,x2. (Round b, to the nearest integer and b, to two decimal places and b, to three decimal places.) ý = (b) Use a = 0.01 to test for a significant relationship. State the null and alternative hypotheses. 0 = 29 = 'q - °g :°H O H.: One or more of the parameters is not equal to zero. O Ho: bị = b2 = 0 H: One or more of the parameters is not equal to zero. O H: One or more of the parameters is not equal to zero. H: b, = b2 = 0 O Ho: One or more of the parameters is not equal to zero. H: bo = b, = b2 = 0
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 = What is your conclusion? O Do not reject Hn. We conclude that the relationship is significant. O Do not reject H.. We cannot conclude that the relationship is significant. O Reject Hn. We conclude that the relationship is significant. O Reject Ho. We cannot conclude that the relationship is significant. (c) Base on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.) vehicles per hour
Transcribed Image Text: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 = What is your conclusion? O Do not reject Hn. We conclude that the relationship is significant. O Do not reject H.. We cannot conclude that the relationship is significant. O Reject Hn. We conclude that the relationship is significant. O Reject Ho. We cannot conclude that the relationship is significant. (c) Base on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.) vehicles per hour
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