A highway department is studying the relationship between traffic flow and speed
ID: 2906773 • Letter: A
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.
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).
Explanation / Answer
Call:
lm(formula = y ~ x + m)
Residuals:
1 2 3 4 5 6
-5.673 -1.673 20.378 -8.622 6.796 -11.204
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 567.60204 114.34894 4.964 0.0157 *
x 29.88776 6.05883 4.933 0.0160 *
m -0.28735 0.07539 -3.811 0.0318 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 15.23 on 3 degrees of freedom
Multiple R-squared: 0.9814, Adjusted R-squared: 0.969
F-statistic: 79.06 on 2 and 3 DF, p-value: 0.002541
The above is the summary of this regression problem.
regression equation: y= 567.602 + 29.8776* x + -.2735* x2
Adjusted R-squared: 0.969 i.e 96.9% of Total variability is explained.
F-statistic: 79.06
p-value: 0.002541 < 0.01 Hence we reject Ho at 99% level of confidence
Our regression is s.t
y= 567.602 + 29.8776* x + -.2735* x2
where y: Traffic flow and x:vehicle speed
when x=39 miles per hour
y= 567.602 + 29.8776* 39 + -.2735* 392
y = 1316.83
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