Question

c) Suppose that you have at your disposal the information below for each of 30 drivers. Propose a model (including a very brief indication of symbols used to represent independent variables) to explain how miles per gallon vary from driver to driver on the basis of the factors measured.

Information:

1. miles driven per day

2. weight of car

3. number of cylinders in car

4. average speed

5. number of passengers

d) Use the sum of square residuals (SSR) to determine which of the following two lines fit the data better.

Ordered pairs: (1,-2), (3, 4), (-4,0)

Line 1: y = 3x-4

Line 2: y = -x+2

Line 3: y = 2x+1

Line 4: y = -2x-3

Answer 1

(c) here we use multiple linear regression to explain how miles per gallon vary from driver to driver on the basis of the factors measured and

miles_per_gallon= b0+b1*miles_driven_per_day+b2*weight_of_car+b3*number_of_cylinders_in_car+b4*_average_speed+b5*number_of_passengers

we have to find the coefficient of b0,b1nb2,b3,b4,b5 from the data available for 30 drivers

(d)line 2 is best among four line as the SSE=e2*e2=29 is least among four lines.

	x	y	line1	line2	line3	line4	e1=y-line1	e2=y-line2	e3=y-line3	e4=y-line4	e12	e22	e32	e42
	1	-2	-1	3	3	-5	-1	-5	-5	3	1	25	25	9
	2	4	2	4	5	-7	2	0	-1	11	4	0	1	121
	-4	0	-16	-2	-7	5	16	2	7	-5	256	4	49	25
sum=	-1	2	-15	5	1	-7	17	-3	1	9	261	29	75	155