Question

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized.

y = B 0 + B 1 x + B₂x 2 + E

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)
1,256	35
1,329	45
1,226	30
1,335	50
1,349	55
1,124	25

Enter negative values as negative, if necessary.

Show the estimated regression equation (to 3 decimals, if necessary).
y = ------ + ----------  x + ------------- x 2

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?
Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 6  
Using  = .01, what is your conclusion?
SelectConclude a curvilinear relationship exists for traffic flow and speedCannot conclude a curvilinear relationship exists for traffic flow and speedItem 7  

Predict the traffic flow in vehicles per hour for a speed of 39 miles per hour (to the nearest whole number).

Answer 1

y = c(1256,1329,1226,1335,1349,1124)

x = c(35,45,30,50,55,25)

model = lm(y~poly(x,2))           # or   lm(y~x+I(x^2))  

round(coef(model),3)              # Reg Coefficients

summary(model)$r.squared          # R^2

summary(model)$fstatistic[1]      # Fstatistic

anova(model)$'Pr(>F)'[1]          # Pvalue

predict(model,data.frame(x=39))   # Predicted value