Question

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized. where traffic flow in vehicles per hour 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 () 1257 36 1329 45 1227 30 1336 50 1349 55 1124 25 a. Use the data to compute the coefficients of this estimated regression equation (to decimals). Enter negative value as negative number. (Create the variable first using Data/Transform

Answer 1

ŷ = 0.1286X - 123.2175 ;

R = 0.9465

R² = 0.8958

Explanation:

Given the data:

Traffic Flow, X : ()

1257

1329

1227

1336

1349

1124

Vehicle speed, Y () :

36

45

30

50

55

25

The estimated regression equation using a linear regression calculator is given thus:

ŷ = 0.1286X - 123.2175

According to the general linear regression formula :

y = mx + c

Where ; y = predicted variable (vehicle speed)

x = predictor variable (traffic flow)

Slope, m = 0.1286

Intercept, c = 123.2175

The correlation Coefficient, R = 0.9465, This depicts a strong positive relationship between traffic flow and vehicle speed.

The Coefficient of determination, R² = 0.9465² = 0.8958 ; This means about 89.5% of variation in Vehicle speed can be explained by the regression line.