Question

The accompanying data are the caloric contents and the sugar contents​ (in grams) of 11 ​high-fiber breakfast cereals. What is the equation of the regression line? Use the regression equation to predict the value of y for each of the given​ x-values.

a) x=150 b)x=90 c)x=175 d)x=198

Calories (x): 140 190 170 170 170 180 190 200 190 160 160

Sugar (y): 6 9 6 9 10 16 13 18 20 10 10

Answer 1

	Calories (X)	Sugar (Y)	X * Y
	140	6	840	19600	36
	190	9	1710	36100	81
	170	6	1020	28900	36
	170	9	1530	28900	81
	170	10	1700	28900	100
	180	16	2880	32400	256
	190	13	2470	36100	169
	200	18	3600	40000	324
	190	20	3800	36100	400
	160	10	1600	25600	100
	160	10	1600	25600	100
Total	1920	127	22750	338200	1683

Equation of regression line is


b = 0.19

a =( 127 - ( 0.1896 * 1920 ) ) / 11
a = -21.556

Equation of regression line becomes \hat{Y} = -21.5562 + 0.1896X

When X = 150
= -21.556 + 0.19 X
= -21.556 + 0.19 * 150
= 6.94

When X = 90
= -21.556 + 0.19 X
= -21.556 + 0.19 * 90
= -4.46

When X = 175
= -21.556 + 0.19 X
= -21.556 + 0.19 * 175
= 11.69

When X = 198
= -21.556 + 0.19 X
= -21.556 + 0.19 * 198
= 16.06