Question

1)

Given the following information, what is the least squares estimate of the y-intercept?

x	y
2	50
5	70
4	75
3	80
6	94

a)3.8 b)5 c) 7.8 d) 42.6

2) A least squares regression line

a) can only be determined if a good linear relationship exists between x and y.

b) ensures that the predictions of y outside the range of the values of x are valid.

c) implies a cause-and-effect relationship between x and y.

d) can be used to predict a value of y if the corresponding x value is given.

3) Regression analysis was applied between sales (in $1,000s) and advertising (in $100s) and the following regression function was obtained.

ŷ = 900 + 6x

Based on the above estimated regression line, if advertising is $10,000, find the point estimate for sales (in dollars).

a) $1,500 b) $60,900    c) $907,000    d) $1,500,000

Answer 1

	X	Y	X * Y	X2	Ŷ
	2	50	100	4	58.2
	5	70	350	25	81.6
	4	75	300	16	73.8
	3	80	240	9	66
	6	94	564	36	89.4
Total	20	369	1554	90	-24516.9

Equation of regression line is Ŷ = a + bX
b = ( n Σ(XY) - (ΣX* ΣY) ) / ( n Σ X2 - (ΣX)2 )
b = ( 5 * 1554 - 20 * 369 ) / ( 5 * 90 - ( 20 )2)
b = 7.8

a =( ΣY - ( b * ΣX ) ) / n
a =( 369 - ( 7.8 * 20 ) ) / 5
a = 42.6
Equation of regression line becomes Ŷ = 42.6 + 7.8 X

Y intercept

Part 2)

d) can be used to predict a value of y if the corresponding x value is given.

Part 3)

ŷ = 900 + 6x

ŷ = 900 + 6 ( 10000 )

b) $60,900