Question

120 Maine lakes were analyzed for mercury level (ppm) and lake elevation (feet).

a. Consider the simple linear model, E(y) = Beta_0 + Beta_1(x), where y = mercury level and x = elevation. Is there evidence that mercury level decreases linearly as elevation increases?

b. Conduct a residual analysis for the linear model. Do the assumptions on epsilon appear to be satisfied?

LAKE	MERCURY	ELEVATION
ALLIGATOR.P	0.025	1494
DIMMICK.P(LITTLE)	0.05	1390
HOSMER.P	0.071	212
PENNINGTON.P	0.08	904
INDIAN.P(BIG)	0.09	1209
BUBBLE.P	0.1	331
SANDY.RIVER.P(LOWER)	0.1	1690
TOGUE.P	0.11	1189
TOGUS.P	0.12	180
CHASE.P(FIRST)	0.13	995
OTTER.P	0.13	1633
SPENCER.P	0.14	1045
OTTER.P	0.16	1373
VARNUM.P	0.16	756
BEN.ANNIS.P	0.18	122
CHUB.P	0.18	1095
SYMMES.P	0.18	499
WEBBER.P	0.18	118
SEWALL.P	0.19	15
WEYMOUTH.P	0.19	296
DAMARISCOTTA.L	0.21	54
LONG.P	0.21	1157
DUCK.L	0.22	519
ROACH.P(SECOND)	0.22	1271
ROWE.P	0.22	1203
BRAINARD.P	0.23	270
PURGATORY.P(LITTLE)	0.23	177
GREENWOOD.P(LITTLE)	0.24	683
HAY.L	0.24	653
CHANDLER.L	0.25	824
WOOD.P(LITTLE.BIG)	0.25	1244
CHURCHILL.L	0.26	922
SQUAW.P(BIG)	0.26	1486
BEAVER.P	0.27	397
GRAND.L(WEST)	0.28	298
KNIGHT.P	0.28	101
CARLTON.BOG(POND)	0.29	203
COBBOSSEECONTEE.L	0.29	165
UMBAGOG.L	0.29	1245
BRACKETT.L	0.31	446
MEDDYBEMPS.L	0.32	170
KINGSBURY.P	0.34	929
FLYING.P	0.35	345
KEENE.L	0.35	195
FISH.P	0.36	1503
FISHER.P(BIG)	0.36	1150
PEASE.P	0.36	377
THIRD.L	0.36	751
LILY.P	0.37	146
NEQUASSET.P	0.37	17
SANDY.RIVER.P(MID)	0.37	1700
SLY.BROOK.L(SECOND)	0.37	637
PATTEE.P	0.38	141
CROSS.L	0.39	578
LONG.P	0.4	390
BURNT.P	0.41	328
CRYSTAL(BEALS).P	0.41	328
PLEASANT.L	0.41	319
SENNEBEC.P	0.41	87
SUNDAY.P	0.41	1409
WADLEIGH.P	0.41	913
BRANCH.P(UPPER.MID)	0.43	341
CHASE.L	0.43	819
DEBSCONEAG.L(4TH)	0.43	634
JUMP.P	0.43	312
UMCOLCUS.L	0.43	882
EAGLE.L	0.44	574
ROUND.P	0.44	474
LAMBERT.L	0.45	419
LOVEWELL.P	0.45	357
SHIN.P(LOWER)	0.47	778
MOOSELEUK.L	0.48	846
PLEASANT.L	0.48	232
BURDEN.P	0.49	639
WIGHT.P	0.49	67
ROUND(GREY).P	0.51	269
ROBERTS&WADLEY.PDS	0.52	271
NORTH.P	0.54	487
PASSAGASSAWAUKEAG.L	0.55	304
PORTLAND.L	0.56	446
ANASAGUNTICOOK.L	0.57	402
BRANCH.P(EAST)	0.57	910
EMBDEN.P	0.57	416
ROUND.P	0.57	34
BRANCH.L(SOUTH)	0.58	227
SECOND.L	0.58	247
PLEASANT.P	0.6	362
JERRY.P	0.62	717
NORTH.P	0.62	510
BELDEN.P	0.66	350
PINE.P(BIG)	0.67	1097
PITCHER.P	0.67	204
ROCKY.P	0.68	312
FOLSOM.P	0.71	221
GRAHAM.L	0.71	102
GRANGER.P	0.73	524
BAUNEAG.BEG.L	0.75	205
BALCH&STUMP.PONDS	0.77	557
BURNT.MEADOW.P	0.77	374
JACOB.BUCK.P	0.77	205
OSSIPEE.L(LITTLE)	0.77	311
BASKAHEGAN.L	0.79	417
CANADA.FALLS.L	0.79	1235
HORSESHOE.L	0.8	454
BRADBURY(BARKER).L	0.81	449
TRAVEL.P	0.82	204
ORANGE.L	0.86	76
KEEWAYDIN.L	0.89	676
HICKS.P	0.9	683
CEDAR.L	0.91	500
CHAIN.OF.PONDS	0.91	1273
EAST.P	0.94	263
FIELDS.P	0.96	109
BOTTLE.L	1.05	298
ALLEN.P	1.08	425
MACHIAS.L(FOURTH)	1.12	311
MOLUNKUS.L	1.12	354
FOREST.L	1.22	276
RANGE.P(LOWER)	1.25	306
HODGDON.P	2.5	50

Answer 1