Answer to Question #213098 in Statistics and Probability for Love

Question

There has been a study saying that the speed of a vehicle before it met an accident can be estimated by distance of the skid marks it has created during full braking,consider the table below

MPH Braking Distance(ft)

20 20

30 45

40 81

50 133

60 205

80 411

Assume MPH is going to be used to predict stopping distance.

1.Find the regression equation.

2.Interpret the slope and the y-intercept of the equation.

3.Find the braking distance when MPH=45.

4.Find the braking distance when MPH=100.

5.what would you say if we proceed on predicting beyond the data values?

Answer 1

1. y=a+bx

By using Excel:

=INTERCEPT(B2:B7,A2:A7)

a= -151.9

=SLOPE(B2:B7,A2:A7)

b=6.45

y=6.45x-151.9

2. The slope b=6.45>0. This states that the braking distance increases as MPH increases. These two variables are positively correlated. It also gives the extent to which the braking distance increases per unit change in MPH. Hence we have a 6.45-fold increase in braking distance for a unit change in MPH. The y-intercept is a= -151.9. This represents the value of y when x=0. This is a measure of braking distance when MPH is 0.

3. $y(45) = 6.45 \times 45 -151.9=138.35$

4. $y(100) = 6.45 \times 100 - 151.9 = 493.1$

5. The liner model was built on the range of MPH between 20 and 80. It can be extended to calculate braking distance and MPH beyond this range. However, this is based on the assumption that the liner model holds true beyond this range. There can be a huge error in the range beyond the range on which the model is built.