Question

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized 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) 1,256 1,330 1,226 1,335 1,350 1,125 Vehicle Speed (x) 35 35 50 25 Enter negative values as negative, if necessary a. Show the estimated regression equation (to 3 decimals, if necessary) 433 37.4 x+0.383 b. What is the value of the coefficient of determination (to 3 decimals)? Note: report R 2 between 0 and 1 What is the value of the F test statistic (to 2 decimals)? What is the p-value? Select using α Select .01, what is your conclusion? c. Predict the traffic flow in vehicles per hour for a speed of 38 miles per hour (to the nearest whole number)

Answer 1

applying polynomial regression"

a) yhat =620.151+25.822*x+(-0.228)*x²

b)

value of coefficient of determiation =0.984
F test statistic =90.61

p value=0.0021

c) predicted value =620.151+25.822*38+(-0.228)*38² =1272