Question

In: Statistics and Probability

Motorists travelling at higher rates of speed or driving too fast for conditions have less time...

Motorists travelling at higher rates of speed or driving too fast for conditions have less time to react, take longer to stop in an emergency, and don’t always see warning and advisory signs. The faster your speed, the more distance you need to stop. It increases even more in wet or icy road conditions. Following tables shows the speed of a vehicle and total stopping distance (reaction + braking) in ideal weather condition. It is determined that approximately 98.77% of the variation in the total stopping distance can be explained by the variation in the speed.

Speed (km/h)	Total Stopping Distance (meter)
30	21
40	25.70
50	34.80
60	45.20
70	56.70
80	72.00
90	83.00
100	100.90
110	113.94
120	135

(a) Determine the five-number summary of the Total Stopping Distance. (1 mark)

(b) Determine if the Total Stopping Distance contains outliers .

(c) Calculate the least squares regression equation for predicting the Total Stopping Distance from the speed of a vehicle.

(d) Calculate the residual if the speed of your vehicle is 70 km/h. (1 mark)

Expert Solution

a) five-number summary of the Total Stopping Distance

Statistics
Variable	Minimum	Q1	Median	Q3	Maximum
Total Stopping Distance (meter)	21	32.5	64.3	104.2	135

b)

Determine if the Total Stopping Distance contains outliers

we will draw boxplot to check is their any outliers present or not

so from above boxplot we can see that their is no point outside of boxplot. So Total Stopping Distance do not have any outliers.

c)the least squares regression equation for predicting the Total Stopping Distance from the speed of a vehicle

Regression Equation

Total Stopping Distance (meter) = -26.76 + 1.2745 Speed (km/h)

(d) Calculate the residual if the speed of your vehicle is 70 km/h.

Total Stopping Distance (meter) = -26.76 + 1.2745 Speed (km/h)

Total Stopping Distance (meter) = -26.76 + 1.2745*70

Total Stopping Distance (meter) = 62.46 meter

Residual = Observed value of Total Stopping Distance (meter) when speed is 70(km/h) -

Fitted value of Total Stopping Distance (meter) when speed is 70(km/h) using regression equation.

Residual = 56.70 - 62.46 = - 5.76

orchestra answered 2 years ago

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Motorists travelling at higher rates of speed or driving too fast for conditions have less time...

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