Question

g 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 = 0.947

r² = 0.896

Explanation:

Given the data:

Traffic Flow, X : ____Vehicke speed ;Y()

1257 ______________36

1329 ______________45

1227 ______________30

1336 ______________50

1349 ______________55

1124 ______________ 25

The estimated regression equation using a linear regression calculator based on the data given above is given thus:

ŷ = 0.1286X - 123.2175

Where ;

y = dependent variable (vehicle speed)

x = predictor variable (traffic flow)

Slope = 0.1286

Intercept = 123.2175

The correlation Coefficient, R, obtained using the correlation Coefficient calculator is 0.9465, This depicts a very strong positive relationship between traffic flow and vehicle speed.

The Coefficient of determination, R² which is the squared value of the correlation Coefficient = 0.9465² = 0.8958 gives the proportion of explained variance ; This means about 89.5% of variation in Vehicle speed can be explained by the regression line.