A highway department is studying the relationship between traffic flow and speed

Question

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

y =B 0 + B1 x +B 2 x2 + 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 + ------------ x2

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? Using = .01, what is your conclusion?

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

-------------

Explanation / Answer

> y <- c(1256,1329,1226,1335,1349,1124);y
[1] 1256 1329 1226 1335 1349 1124
> x <- c(35,45,30,50,55,25);x
[1] 35 45 30 50 55 25
> regressor <- lm(y ~ x)
> summary(regressor)

Call:
lm(formula = y ~ x)

Residuals:
1 2 3 4 5 6
20.667 24.667 25.167 -3.833 -24.333 -42.333

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 993.833 49.940 19.901 3.76e-05 ***
x 6.900 1.205 5.725 0.00461 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 31.89 on 4 degrees of freedom
Multiple R-squared: 0.8912, Adjusted R-squared: 0.864
F-statistic: 32.77 on 1 and 4 DF, p-value: 0.004609

a) y = 993.833 + 6.900 * x

b) coefficient of determinationis 0.8912

c) value of F- statistic = 32.77

d) p value is 0.00469

it is less than level of significance so thelinear regression equation is effective so vhecichle speed is important in traffic flow

e)> y <- 993.8+ 6.9 * 39
> y
[1] 1262.9

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