A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized.ŷbo+b₁x + b₂x²whereThe following data were collected during rush hour for six highways leading out of the city.y = traffic flow in vehicles per hour* = vehicle speed in miles per hourTraffic Flow (y)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 hour12571329122713361349Vehicle Speed (2)35112540354530a. Use the data to compute the coefficients of this estimated regression equation (to 4 decimals). Enter negative value as negative number. (Create the ² variable first using Data/Transform Data/Square.)bo =b₁ =b₂ =b. Using a = 0.01, test for a significant relationship.F=(to 4 decimals)55

It is given that traffic flow in vehicles per hour is denoted as y and the vehicle speed in miles per hour is denoted as x.a. By using the EXCEL, the estimated regression equation is obtained below: Enter the data and create the new variable x2 by squaring the vehicle speed. Now go to DATA > Data analysis > Regression > Choose the y range and x range. Mark labels and click OK. The output is, From the output, the coefficients are b0=-186.5247,b1=63.2627,b2=-0.6441. Thus, the coefficients of the estimated regression equation is b0=-186.5247,b1=63.2627,b2=-0.6441.b. From the EXCEL output, the F test statistic is 45.7105, and p-value is 0.0057. Thus, the F test statistic is 45.7105, and p-value is 0.0057. Since the p-value is less than the given level of significance indicating that there is relationship is significant. Thus, the relationship is significant.c. The regression equation is, y^=b0+b1x+b2x2=-186.5247+63.2627x-0.6441x2 The estimated traffic flow in vehicles per hour at a speed of 38 miles per hour is, y^=-186.5247+63.262738-0.6441382=-186.5247+2403.9826-930.0804≈1287.38 Thus, the estimated traffic flow in vehicles per hour at a speed of 38 miles per hour is 1,287.38.