Question

The accompanying data are the caloric contents and the sugar contents​ (in grams) of

1111

​high-fiber breakfast cereals. Find the equation of the regression line. Then construct a scatter plot of the data and draw the regression line. Then use the regression equation to predict the value of y for each of the given​ x-values, if meaningful. If the​ x-value is not meaningful to predict the value of​ y, explain why not.

​(a) xequals=150150 cal

​(b) xequals=9090 cal

​(c) xequals=175175 cal

​(d) xequals=198198 cal

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Answer 1

Scatter plot:

	X	Y	X^2	Y^2	XY
	140	6	19600	36	840
	190	10	36100	100	1900
	170	6	28900	36	1020
	170	9	28900	81	1530
	180	10	32400	100	1800
	180	16	32400	256	2880
	200	14	40000	196	2800
	200	17	40000	289	3400
	190	19	36100	361	3610
	160	10	25600	100	1600
	170	11	28900	121	1870
SUM	1950	128	348900	1676	23250
n	11
Mean	177.2727	11.63636364
SSxx	3218.182	Sum(x^2) - ((Sum(x))^2 /n)	SSR	97.1302	slope * Ssxy	MSR	97.1302
Ssyy	186.5455	Sum(y^2) - ((Sum(y))^2 /n)	SSE	89.41525	SST-SSR	MSE	9.935028
Ssxy	559.0909	Sum(xy) - (Sum(x)*Sum(y)/n)	SST	186.5455	Ssyy	F	9.77654
slope	0.173729	Ssxy/SSxx
intercept	-19.161	Mean Y - Mean X * Slope
Se	3.151988	SQRT(SSE/(n-2))
Sb1	0.055562	Se/SQRT(SSxx)
r	0.721581	SSXY/SQRT(SSxx*Ssyy)
r^2	0.520678

Y = -19.161 + 0.1737 * X

a )

If X = 150

Y = -19.161 + 0.1737 * X

Y = -19.161 + 0.1737 * 150 = 6.894

b)

If X = 90

Y = -19.161 + 0.1737 * X

Y = -19.161 + 0.1737 * 90 = -3.528

it is not meaningful, because sugar decreasing while calories are decreasing

c)

If X =175

Y = -19.161 + 0.1737 * X

Y = -19.161 + 0.1737 * 175 = 11.2365

d)

If X =198

Y = -19.161 + 0.1737 * X

Y = -19.161 + 0.1737 * 198 = 15.2316

Except X = 90 other values are meaningful because Y value increasing with X value