Question

CENGAGE | MINDTAP Q Search this course Julia Chapter 16 Assignment A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized. y = Bo+ B 1x + B 2x2 + € 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) 1,257 1,329 1,227 1,336 1,350 1,124 Enter negative values as negative, if necessary. a. Show the estimated regression equation (to 3 decimals, if necessary). y = 890.2 + X + x2 b. What is the value of the coefficient of determination (to 3 decimals)? Note: report R2 between 0 and 1. 0.9714 What is the value of the F test statistic (to 2 decimals)? 162.14 What is the p-value? less than .01 Using a = .01, what is your conclusion? Conclude a curvilinear relationship exists for traffic flow and speed c. Predict the traffic flow in vehicles per hour for a speed of 38 miles per hour (to the nearest whole number). 12

Answer 1

a) 672.583 + (22.218) X - 0.171 (x2) | 672.583) + [22.218 *(x) - 0.171)*(x2) Û = 672.583 + 22.218(x) -0.171 (x3) b) I Coefficient of defermination = 0.9899 = 10.989 E test statistic = [148.379 ) = [148.38 p-value [ooool - As pvalue 0.00) e Qarool so we reject Ho. We conclude a curvilinear relationship exists for traffic flow and speed. 9 Û 672.583 + 22.218 (38) + (-0.171) (38) 1269.943 = 1269.943 = | 1270 û = 1269 - 1270