Is Depth (x3) a statistically significant predictor of Arsenic Level? Test using

Question

Is Depth (x3) a statistically significant predictor of Arsenic Level? Test using alpha = 1%

LATITUDE LONGITUDE DEPTH-FT ARSENIC_Level 23.78865 90.65216 60 331 23.78860 90.65231 45 302 23.78877 90.65223 50 232 23.78796 90.65172 45 193 23.78926 90.65248 125 232 23.79204 90.61401 150 19 23.78166 90.62499 60 33 23.78164 90.62498 55 2 23.78186 90.62482 46 1 23.78216 90.62457 60 23 23.78157 90.62460 60 111 23.77974 90.61804 30 92 23.77966 90.61804 30 71 23.77952 90.61771 55 116 23.77947 90.61786 45 114 23.77957 90.61754 40 74 23.76510 90.61761 130 276 23.76538 90.61683 45 35 23.76546 90.61642 65 65 23.76540 90.61559 40 15 23.79253 90.60987 120 27 23.79387 90.60992 120 25 23.79316 90.61022 60 12 23.79447 90.60960 110 21 23.79700 90.61071 80 1 23.79668 90.61082 110 1 23.79649 90.61091 120 1 23.79626 90.61108 150 1 23.79613 90.61095 120 1 23.79704 90.60810 65 122 23.79726 90.60812 75 135 23.79657 90.60871 80 112 23.79583 90.60813 95 2 23.79417 90.60879 95 1 23.78778 90.60090 120 1 23.78809 90.60112 120 1 23.78812 90.60081 120 1 23.79824 90.61072 150 3 23.79892 90.60995 35 6 23.80002 90.61000 165 1 23.80025 90.61088 170 2 23.79775 90.64724 60 100 23.78816 90.64508 35 75 23.78728 90.64529 100 176 23.78567 90.64501 70 131 23.78561 90.64547 45 111 23.78553 90.64508 35 160 23.78259 90.63667 50 194 23.78266 90.63672 40 109 23.78290 90.63666 45 74 23.78235 90.63653 70 178 23.78037 90.63838 46 333 23.78049 90.63834 45 207 23.78010 90.63809 75 134 23.78011 90.63785 46 302 23.78005 90.63755 45 379 23.78483 90.61480 45 45 23.78504 90.61576 45 45 23.78501 90.61585 45 50 23.78472 90.61578 45 35 23.78453 90.61573 45 35 23.78090 90.61643 45 1 23.78045 90.61630 60 121 23.78060 90.61660 60 31 23.78086 90.61689 35 23 23.78063 90.61683 45 78 23.77684 90.61634 25 58 23.77678 90.61636 120 109 23.77743 90.61783 32 51 23.77796 90.61864 32 54 23.77727 90.61584 45 1 23.77733 90.61559 40 2 23.77728 90.61541 40 1 23.77720 90.61526 60 2 23.77722 90.61527 70 1 23.77627 90.61636 36 44 23.77529 90.61285 55 58 23.77534 90.61282 35 30 23.77608 90.61254 55 6 23.77590 90.61243 35 3 23.77620 90.61245 120 18 23.77996 90.60705 70 469 23.77355 90.60440 40 12 23.77324 90.60328 45 29 23.77195 90.60310 45 6 23.77220 90.60435 65 67 23.77187 90.60293 45 10 23.77178 90.60273 40 1 23.77151 90.60323 45 25 23.77133 90.60262 55 44 23.76969 90.60218 45 4 23.76694 90.60359 36 89 23.79993 90.62177 60 44 23.80019 90.62187 60 46 23.79958 90.62336 75 27 23.79949 90.62338 75 24 23.79942 90.62340 75 24 23.78225 90.63671 70 114 23.78941 90.63236 45 201 23.78855 90.63560 60 265 23.78898 90.63624 60 159 23.78921 90.63658 45 287 23.78906 90.63707 70 229 23.78889 90.63725 60 195 23.77949 90.63186 72 93 23.78377 90.62924 75 28 23.78327 90.62947 37 15 23.78313 90.62951 45 25 23.78335 90.62984 52 144 23.78366 90.62966 50 14 23.77798 90.63119 36 27 23.77613 90.63261 40 229 23.77993 90.63071 35 61 23.77537 90.63539 45 269 23.77532 90.63567 60 241 23.77494 90.63603 90 544 23.77566 90.62980 45 36 23.77201 90.62962 40 18 23.77163 90.62967 60 5 23.77171 90.62964 45 25 23.77164 90.62956 55 109 23.77139 90.62951 45 28 23.76930 90.62465 50 17 23.76938 90.62460 46 51 23.76987 90.62444 60 522 23.77001 90.62419 50 172 23.76886 90.62172 45 65 23.76414 90.61947 45 39 23.75468 90.61206 200 1 23.75485 90.61209 160 231 23.75467 90.61205 60 225 23.75497 90.61228 50 36 23.75518 90.61210 80 89 23.75563 90.61138 50 99 23.75591 90.61147 35 126 23.75590 90.61121 50 154 23.75563 90.61094 60 128 23.75593 90.61055 45 129 23.78804 90.61878 45 153 23.78806 90.61879 45 142 23.78783 90.61905 50 201 23.78778 90.61904 60 156 23.78967 90.62636 50 202 23.79012 90.62604 50 92 23.79011 90.62589 50 81 23.79004 90.62606 40 399 23.79073 90.62590 50 42 23.79100 90.62636 50 95 23.79084 90.62651 40 189 23.79076 90.62655 55 114 23.79075 90.62677 60 216 23.79044 90.62676 50 150 23.77990 90.62759 45 140 23.77969 90.62740 75 129 23.77972 90.62718 45 73 23.77979 90.62703 45 1 23.77970 90.62689 45 48 23.79270 90.62264 45 55 23.79273 90.62327 110 98 23.79256 90.62334 72 43 23.79263 90.62359 52 20 23.75901 90.61638 25 28 23.75885 90.61595 25 75 23.75949 90.61576 45 59 23.75971 90.61615 70 34 23.75969 90.61548 80 77 23.76186 90.61598 45 21 23.76213 90.61524 45 3 23.76240 90.61528 45 38 23.76224 90.61550 55 125 23.76188 90.61637 60 125 23.79083 90.60573 120 1 23.79078 90.60565 120 1 23.79091 90.60572 140 1 23.79102 90.60582 125 1 23.79067 90.60611 120 1 23.79168 90.60675 155 1 23.79185 90.60683 140 1 23.79172 90.60644 175 1 23.79222 90.60703 140 1 23.79195 90.60709 140 1 23.80075 90.60625 115 1 23.80057 90.60584 105 2 23.80075 90.60595 105 1 23.80034 90.60594 105 1 23.80033 90.60608 105 1 23.79758 90.60825 80 110 23.78803 90.61049 30 1 23.78920 90.60990 30 1 23.78735 90.60984 25 1 23.78852 90.61062 25 1 23.78771 90.61135 30 1 23.78794 90.61143 30 1 23.78843 90.61157 35 1 23.78841 90.61147 30 3 23.78819 90.61141 30 1 23.78921 90.61497 35 7 23.78997 90.61511 45 149 23.78989 90.61564 25 50 23.79004 90.61569 25 37 23.79121 90.61438 170 3 23.79236 90.61446 35 7 23.79191 90.61490 148 1 23.79197 90.61499 145 9 23.79220 90.61486 192 9 23.78221 90.61176 45 416 23.78178 90.61102 40 148 23.78228 90.61114 35 97 23.78906 90.61157 25 1 23.77815 90.60065 195 32 23.77878 90.60051 145 1 23.77813 90.60000 130 1 23.77770 90.59903 165 1 23.77775 90.59890 60 295 23.77743 90.59872 120 1 23.77796 90.59884 130 1 23.77802 90.59882 60 306 23.77439 90.59385 70 161 23.77429 90.59293 479 23.77185 90.59169 45 241 23.77049 90.59083 65 151 23.77106 90.58796 225 32 23.77093 90.58861 35 90 23.76876 90.59453 65 90 23.76883 90.59483 55 77 23.76917 90.59467 60 92 23.76486 90.60066 50 149 23.76458 90.60092 120 74 23.76458 90.60125 45 74 23.76467 90.60128 65 82 23.76413 90.60165 72 268 23.79041 90.63648 45 282 23.79031 90.63624 60 247 23.79010 90.63634 50 111 23.79044 90.63661 45 261 23.78969 90.63656 60 447 23.78778 90.60070 130 1 23.78779 90.60082 130 1 23.80159 90.63065 180 9 23.80206 90.63094 160 2 23.80196 90.63134 45 6 23.80279 90.63223 45 8 23.80318 90.63262 50 9 23.78470 90.60147 135 1 23.78521 90.60157 135 1 23.78519 90.60134 120 1 23.78531 90.60165 135 1 23.78824 90.60776 150 1 23.78826 90.60787 125 1 23.78881 90.60814 45 40 23.78909 90.60843 160 4 23.77795 90.60395 145 15 23.77839 90.60394 135 15 23.77786 90.60365 130 17 23.77810 90.60310 175 15 23.77799 90.60311 75 498 23.77490 90.59332 60 105 23.77450 90.59271 60 294 23.77043 90.58699 120 54 23.77054 90.58662 60 109 23.76933 90.58696 125 71 23.76774 90.58548 45 283 23.76778 90.58555 60 245 23.76537 90.59243 45 142 23.76542 90.59270 45 516 23.76475 90.59249 45 174 23.76457 90.59252 45 301 23.79015 90.63165 45 226 23.79334 90.62288 50 1 23.76508 90.62943 80 163 23.76653 90.62932 25 131 23.80115 90.61052 195 1 23.76617 90.63099 70 50 23.76620 90.63118 70 49 23.79001 90.64591 45 34 23.78976 90.64615 90 86 23.78975 90.64623 50 38 23.79007 90.64600 45 93 23.79022 90.64663 60 68 23.79807 90.64681 45 212 23.79489 90.65151 40 48 23.79519 90.65165 40 52 23.79546 90.65153 30 172 23.79880 90.64891 50 60 23.79896 90.64866 30 42 23.79296 90.65995 35 78 23.79265 90.66113 70 140 23.79272 90.66117 40 12 23.79307 90.66143 40 134 23.79239 90.66000 85 178 23.79319 90.66129 45 116 23.79636 90.66059 40 96 23.79367 90.66068 40 127 23.79437 90.65746 55 113 23.79397 90.65882 60 173 23.79544 90.65982 35 80 23.79533 90.65949 40 90 23.79669 90.66116 45 51 23.79659 90.66169 45 69 23.78270 90.64870 75 49 23.78314 90.64878 75 256 23.78324 90.64889 85 341 23.78309 90.64869 60 47 23.78168 90.64714 60 46 23.79920 90.64936 50 155 23.79937 90.64920 50 54 23.79926 90.64981 50 89 23.77412 90.63766 75 255 23.77196 90.63555 45 18 23.77191 90.63567 45 26 23.77186 90.63582 35 38 23.77177 90.63551 40 78 23.77190 90.63537 35 32 23.76576 90.63122 60 175 23.76564 90.63149 45 624 23.77387 90.63892 45 108 23.76584 90.63173 45 108 23.76756 90.63497 60 307 23.76729 90.63605 150 1 23.76779 90.63765 90 105 23.76633 90.63758 65 78 23.76987 90.63498 35 372 23.76351 90.63045 170 2 23.76374 90.63264 42 110 23.76436 90.63032 30 254 23.79818 90.64751 46 126 23.79795 90.64707 45 95 23.79805 90.64745 45 120

Explanation / Answer

We have used Minitab software of regression analysis by that we get output as below

Regression Analysis: ARSENIC_Level versus DEPTH-FT

The regression equation is
ARSENIC_Level = 141 - 0.669 DEPTH-FT

327 cases used, 1 cases contain missing values

Predictor Coef SE Coef T P
Constant 140.61 11.78 11.93 0.000
DEPTH-FT -0.6694 0.1470 -4.56 0.000

S = 106.920 R-Sq = 6.0% R-Sq(adj) = 5.7%

Analysis of Variance

Source DF SS MS F P
Regression 1 237209 237209 20.75 0.000
Residual Error 325 3715353 11432
Total 326 3952562

in every cases we get that p-value=<0.05 so we can claim that there is significant effect of death on this regression at 5% significance.

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