Question

Use the regression equation to predict the number of motor vehicle fatalities in a western state with a population of 4 million people (40 hundred thousand people). Does this answer seem reasonable based on the given data? Why or why not?

• Population (hundreds of thousands) = 3.3277772 + 0.054110317 Motor Vehicle Fatalities

Motor Vehicle Fatalities	Population (hundreds of thousands)
87	7
1117	50
742	47
119	13
264	14
270	9
381	24
449	19
436	36
328	25
659	63
176	5

Answer 1

Solution:

Given regression equation is,

Population=3.3277772+0.054110317*Motor vehicle facilities

This is not correct or not reasonable because, we have to predict the number of motor vehicle facilities in a western state with a forecast of 4 million people.

In this case, our response should be motor vehicle facilities(y) with regressor population(x).

Since the regression equation will be in the form of:

motor vehicle facilities= β0 + β1*Population

For the analysis, the R-code is,

> Motor_vehicle_facility=c(87,1117,742,119,264,270,381,449,436,328,659,176)

> Population=c(7,50,47,13,14,9,24,19,36,25,63,5)

> model=lm(Motor_vehicle_facility~Population)

> model

#OutPut

Call:

lm(formula = Motor_vehicle_facility ~ Population)

Coefficients:

(Intercept)   Population

      74.58        13.25

Therefore, the correct regression eq. is,

motor vehicle facilities= 74.58 + 13.25*Population

and forecast at population=4 Million peoples is,

motor vehicle facilities= 74.58 + 13.25*4

                                          =127.58