Question

A statistical program is recommended. A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: у %3DВо + В,х +е 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) (y) 1,257 35 40 1,327 1,226 30 1,333 45 50 1,350 1,122 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ў - bo + b,x + b,x* (a) Develop an estimated regression equation for the data of the form y = b b,x + bzx*. (Round b to the nearest integer and b, to two decimal places and b, to three decimal places.) y = (b) Use a 0.01 to test for a significant relationship. State the null and alternative hypotheses. о Ho: bo 3D b, %3Db, 3D 0 H: One or more of the parameters is not equal to zero. о Hо: b, 3D b, %3D0 HOne or more of the parameters is not equal to zero. Ho: One or more of the parameters is not equal to zero. Ha: bo b b, = 0 Ho: One or more of the parameters is not equal to zero. На: b, 3D b, 3D о 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? Reject H. We conclude that the relationship is significant Reject H We cannot conclude that the relationship is significant. Do not reject Ho. We cannot conclude that the relationship is significant. Do not reject H. We 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

Answer 1

R codes and output :

  
x=c(35,40,30,45,50,25)
y=c(1257,1327,1226,1333,1350,1122)
z=x*x
f=lm(y~x+z)
summary(f)

Call: Im(formula = y X + z) Residuals: 1 2 3 5 6 -15.771 10.486 16.079 -8.150 3.321 -5.964 Coefficients: Estimate Std. Error t value Pr(>lt) (Intercept) 431.5714 139.1712 3.101 0.0533 37.4093 7.6965 4.861 0.0166 * X -0.3821 0.1021 -3.741 0.0333* Signif. codes: 0 ***' 0.001 "**' 0.01 * 0.05 '0.1' 1 Residual standard error: 15.6 on 3 degrees of freedo m Multiple R-squared: 0.9806, Adjusted R-squared: 0.9677 F-statistic: 75.78 on 2 and 3 DF, p-value: 0.002704 N i

Our answer based on the output :

MBER 13-. 1-10.2421a b) Aw of the la ue r moro paramele is uot equal to 11 test otatiotec 5.78 12 PuRlne Couclusisn 2 Rayct Ho we conclud hat e telatinskrip's gaficant 4(3e)-0 342(2 2 3g 432 1301.472 1301 3-4 . 5