Question

Wins and Earned Run Averages The number of wins and earned run averages (mean number of runs allowed per nine innings pitched) for eight professional baseball pitchers in the 2012 regular season are given below. Round your answers to two decimal places. Find

a) the equation of the regression line and

b) the earned run average predicted for 10 wins.

Wins, x	Earned run average, y
20	2.73
18	3.29
17	2.64
16	3.74
14	3.85
12	4.33
11	3.81
9	5.11

Answer 1

(a)

Regression Equation is y=a+bx

'a' indicates the value of y when x=0. It is called y-intercept

'b' indicates the slope of the regression line and gives a measure of change of 'y' for a unit change in 'x'

For the given probem : y: Earned run average x: Wins

	Wins, x	Earned run average, y	xy	x2
	20	2.73	54.6	400
	18	3.29	59.22	324
	17	2.64	44.88	289
	16	3.74	59.84	256
	14	3.85	53.9	196
	12	4.33	51.96	144
	11	3.81	41.91	121
	9	5.11	45.99	81
Total	117	29.5	412.3	1811

	117
	29.5
	412.3
	1811
n	8

b= -0.1916

a= 6.4897

regression equation : y= 6.4897 - 0.1916x

Earned run average, y = 6.4897 - 0.1916 Wins, x

b) the earned run average predicted for 10 wins.

Substitute x :wins= 10 in the above regression equation.

Earned run average, y = 6.4897 - 0.1916 x 10 = 6.4897 - 1.916 = 4.5737

Earned run average, y = 4.5737 for  10 wins.