Question

A manager wishes to find out whether there is a relationship between the number of radio ads aired per week and the amount of sales of a product. The data for the sample follows.

# of ads (x)	2	5	8	8	10	12
Sales (y)	$2,000	$4,000	$7,000	$6,000	$9,000	$10,000

If the equation of the regression line is y = a + bx, then the value for "a" is:

Round to whole number.  

Answer 1

Solution:

n = 6

	X	Y	XY	X^2	Y^2
	2	2000	4000	4	4000000
	5	4000	20000	25	16000000
	8	7000	56000	64	49000000
	8	6000	48000	64	36000000
	10	9000	90000	100	81000000
	12	10000	120000	144	100000000
SUM	45	38000	338000	401	286000000

We know , for the line y = a + bx,

b denotes the slope of the line and a denotes the y intercept of the line

b = [6 * 286000000 - (45*38000)]/[6*401 - (45²) ] = 834.6457

Now ,

a = [38000 - (834.6457 * 45)]/6 = 73.4908 = 73

Answer : Value for a = 73