Question

Consider the following sample data: 14 30 10 35 26 12 a. Use software to construct a scatterplot. b. Use software to obtain b1 and bo. What is the sample regression equation? c. Find the predicted value for y if x equals 10,15, and 20

Answer 1

	X	Y	X * Y	X^2	Y^2
	22	26	572	484	676
	35	55	1925	1225	3025
	14	30	420	196	900
	10	12	120	100	144
Total	81	123	3037	2005	4745

Scatter Plot 60 50 40 30 20 10 35 40 30 25 20 15 10 0

Equation of regression line is $\hat{Y} = a + bX$
$b = ( n \Sigma XY - \Sigma X \Sigma Y) / ( n\Sigma X^{2} - (\Sigma X)^{2})$

b = 1.498

b = ( 4 * 3037-81 * 123)/(4 * 2005-(81)2)

$a =( \Sigma Y - ( b * \Sigma X) ) / n$
a =( 123 - ( 1.4976 * 81 ) ) / 4
a = 0.424
Equation of regression line becomes

y-0.4236+ 1.4976X

b0 = 0.4236

b1 = 1.4976

Part c)

When X = 10
$\hat{Y}$ = 0.424 + 1.498 X
$\hat{Y}$ = 0.424 + 1.498 * 10
$\hat{Y}$= 15.4

When X = 15
$\hat{Y}$ = 0.424 + 1.498 X
$\hat{Y}$ = 0.424 + 1.498 * 15
$\hat{Y}$ = 22.89

When X = 20
$\hat{Y}$ = 0.424 + 1.498 X
$\hat{Y}$ = 0.424 + 1.498 * 20
$\hat{Y}$ = 30.38