Question

2. (5.03) How sensitive to changes in water temperature are coral reefs? To find out, scientists examined data on sea surface temperatures and coral growth per year at locations in the Red Sea.

Here are the data:

Sea surface temperature	29.65	29.9	30.59	29.51	30.48	30.62	30.88
Growth	2.63	2.59	2.62	2.48	2.24	2.37	2.25

Use your calculator to find:

The mean (±± 0.0001) and standard deviation (±± 0.0001) for sea surface temperature:

              x⎯⎯⎯=x¯=sx=sx=

The mean (±±0.0001) and standard deviation (±± 0.0001) for coral growth:

              y⎯⎯⎯=y¯=sy=sy=

The correlation (±± 0.0001)   r = .

The slope (±± 0.01) of the equation of the least-squares regression line is b =

and the intercept is (±± 0.01) a =

Answer 1

S.No	x	y	X12	Y12	XY
1	29.65	2.63	879.1225	6.9169	77.98
2	29.9	2.59	894.0100	6.7081	77.44
3	30.59	2.62	935.7481	6.8644	80.15
4	29.51	2.48	870.8401	6.1504	73.18
5	30.48	2.24	929.0304	5.0176	68.28
6	30.62	2.37	937.5844	5.6169	72.57
7	30.88	2.25	953.5744	5.0625	69.48
	ΣX	ΣY	ΣX2	ΣY2	ΣXY
total	211.6300	17.1800	6399.9099	42.3368	519.0757

	n=	7.0000
	X̅=ΣX/n	30.2329
	Y̅=ΣY/n	2.4543
	sx=(√(Σx2-(Σx)2/n)/(n-1))=	0.5370
	sy=(√(Σy2-(Σy)2/n)/(n-1))=	0.1694
	Cov=sxy=(ΣXY-(ΣXΣY)/n)/(n-1)=	-0.0541
	r=Cov/(Sx*Sy)=	-0.5950

from above

x¯= 30.2329

sx =0.5370

y^- =2.4543

sy =0.1694

correlation r =-0.5950

slope =r*Sy/Sx =-0.19

intercept =8.13