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(a) (b)
(c) (d) R2 = 98.33% R 2 (adj) = 93.86%
£µ¡š¸É 1 —ŠŸ¨„µ¦Îµ¦ª‹ o°¤¼¨ÁºÊ°Š˜oœ °Š„µ¦Á¦nŠ„µ¦¨µ¥˜´ª °Š 2,4-DCP —oª¥ NZVI ×¥š¸É
(a) „¦µ¢‡ªµ¤´¤¡´œ›r‡ªµ¤œnµ‹³Áž}œ °Š‡nµ‡ªµ¤Ÿ·—¡¨µ—š¸É¤¸„µ¦„¦³‹µ¥Âž„˜· (b) „¦µ¢‡ªµ¤´ ¤¡´œ›r°Š
‡nµ‡ªµ¤Ÿ·—¡¨µ—¨³‡nµÁŒ¨¸É¥ (c) „¦µ¢‡ªµ¤´¤¡´œ›r°Š‡nµ‡ªµ¤Ÿ· —¡¨µ—¨³¨Îµ—´š¸É°Š„µ¦š—¨°Š (d) „¦µ¢
‡ªµ¤´¤¡´œ›r°Š‡nµ„µ¦šÎ µœµ¥Â¨³‡nµ‹¦·Š 宦´‡nµÁž°¦rÁŽÈœ˜rĜ„µ¦¨µ¥˜´ª °Š 2,4-DCP
„µ¦ª· Á‡¦µ³®r„µ¦™—™°¥Á·ŠÁoœ Áž} œ„µ¦«¹„¬µ‡ªµ¤´¤¡´œ›rÁ·ŠÁoœ¦³®ªnµŠ˜´ªÂž¦ž{‹‹´¥ ®¦º°˜´ªÂž¦
°· ¦³ (Factors or Independent Variables; X’s) „´‡nµ˜°œ°Š®¦º°˜´ªÂž¦˜µ¤ (Response or Dependent Variable;
Y) Ĝš¸Éœ¸Ê Á¨º°„čo„µ¦ª· Á‡¦µ³®r„µ¦™—™°¥Á·Š¡®» (Multiple Regression Analysis) ‡º°„µ¦«¹„¬µ‡ªµ¤´¤¡´ œ›r
¦³®ªn µŠ˜´ªÂž¦°· ¦³˜´ÊŠÂ˜n 2 ˜´ª ¹ÊœÅž (k • 2 ˜´ª ¹ÊœÅž) „´˜´ªÂž¦˜µ¤ (y) 1 ˜´ª ‹µ„ o°¤¼ ¨Äœ˜µ¦µŠš¸É 3 µ¤µ¦™
—Š¤„µ¦‡ªµ¤´ ¤¡´œ›rš¸Éšo‹¦·Š—´Šœ¸Ê
y = 12.631 - 8.957x1 + 0.931x2 – 2.534x3 + 0.834x1x2 + 0.424x1x3 + 0.611x2x3 – 1.511x1x2x3 (Eq.1)
ץĜ˜n¨³¡‹œr ‹³¤¸‡nµ P-value nŠ°„´ —Á‹œ Ĝš¸Éœ¸Ê „ε®œ—Ä®o ‡nµÄ—š¸É¤¸‡nµ P-value ¤µ„„ªnµ 0.05 (‡nµ‡ªµ¤ÁºÉ°¤´Éœ
š¸É 95%) ‹³Å¤n¤¸œ´¥Îµ‡´ œ´Éœ‡º°ž{‹‹´¥ x Ä—Ç œ´Êœ Ťn¤¸Ÿ¨„¦³š®¦º °Âš‹³Å¤n¤¸Ÿ¨„¦³š„´  y Á¨¥ ‹µ„˜µ¦µŠš¸É 3
¡ªnµ¤¸Á¡¸¥Š‡nµ x1 ®¦º°œ·— °Š NZVI ¤¸‡nµ P-value = 0.001 Ž¹ÉŠ¤¸ ‡nµœo °¥„ªnµ 0.05 ‹¹Šµ¤µ¦™ª·Á‡¦µ³®rŗoªnµ¤¸Á¡¸¥Š
œ·— °Š NZVI Á¡¸¥Š‡nµÁ—¸¥ªš¸É¤¸Ÿ¨„¦³š˜n °„µ¦¨µ¥˜´ª °Š 2,4-DCP ¨³ž{‹‹´¥°¸„°¥nµŠš¸ÉÁ„º°‹³¤¸Ÿ¨„¦³š˜n °
y œ´Éœ‡º°‡nµ pH (x 3) ×¥¤¸‡nµ P-value = 0.061 Ž¹ÉŠÄ„¨oÁ‡¸¥Š„´ 0.05 ¤µ„ ˜n°¥nµŠÅ¦„Șµ¤‡n µ pH „ÈŤn¤¸œ´¥Îµ‡´˜n°
„µ¦¨µ¥˜´ ª °Š 2,4-DCP ˜µ¤‡nµ P-value š¸É„ε®œ—
˜µ¦µŠš¸É 4 µ¤µ¦™š—°¤¤˜·“µœÂ¦„ (H 0) Á„¸É¥ª„´¤„µ¦„µ¦™—™°¥Á·Š¡®» ŗo‡º°‡nµ™·˜· F ˜o°Š¤¸‡nµ
¤µ„„ªnµ 4.0 (F-value>4.0) ¨³‡nµ P-value ˜o°Š¤¸‡nµœo °¥„ªnµ 0.05 (P-value<0.05) ‹¹Š‹³ž’·Á› H0 宦´
‡ªµ¤´ ¤¡´œ›r°ŠŸ¨„¦³š®¨´ „ (Main Effects) ‡nµ™·˜· F = 57.14 ¨³¤¸‡nµ P-value = 0.004 ‹¹Šž’·Á› H0 œ´É œ‡º°
¤„µ¦™—™°¥µ¤µ¦™¦oµŠÅ—o °¸„œ´¥®œ¹ÉŠ‡º°Ÿ¨„¦³š °Šž{ ‹‹´¥ x Ä—Ç µ¤µ¦™°›· µ¥„µ¦Áž¨¸É¥œÂž¨Š °Š y ŗo
2 1 0 -1 -2
0.99
0.95
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.05
0.01
Standardized Residual
Probability
Normal Probability Plot
(response is % removal)
30 25 20 15 10 5 0
1.5
1.0
0.5
0.0
-0.5
-1.0
Fitted Value
Standardized Residual
Versus Fits
(response is % removal)
12 11 10 9 8 7 6 5 4 3 2 1
1.5
1.0
0.5
0.0
-0.5
-1.0
Observation Order
Standardized Residual
Versus Order
(response is % removal)
30 25 20 15 10 5 0
30
25
20
15
10
5
0
Actual value (% removal)
Predicted value (% removal)
Scatterplot of Predcted value vs Actual value