Download Lecture Notes on Statistics Psychological Research | PSYC 300 and more Study notes Psychology in PDF only on Docsity! x y x² x-1 (x-1)² (x-3) xy y² y-1 (y-1)² (y-3) 4 5 16 3 9 1 20 25 4 16 2 3 6 9 2 4 0 18 36 5 25 3 0 0 0 -1 1 -3 0 0 -1 1 -3 1 4 1 0 0 -2 4 16 3 9 1 7 4 49 6 36 4 28 16 3 9 1 Σx= 4+3+0+1+7 =15 Σy= 5+6+0+4+4 = 19 Σx² = 16+9+0+1+49 = 75 Σy²= 25+36+0+16+16 = 93 (Σx)²= 15*15=225 (Σy)²= (19)²=361 Σx-1= 15-1=14 Σy-1=19-1=18 Σ(x-1)= 3+2-1+0+6=10 Σ(y-1)= 4+5-1+3+3=14 Σ(x-1)²= 9+4+1+0+36=50 Σ(y-1)²= 16+25+1+9+9=60 Σ(x-3)= 1+0-3-2+4=0 Σ(y-3)= 2+3-3+1+1=4 Σx/5 =15/5=3 Σy/5= 19/5=3.8 Σ(x-1)²/5= 50/5=10 Σ(y-1)²/5= 60/5=12 ΣxΣy= (15)(5+6+0+4+4)= ΣxΣy/5= 285/5=57 (15)(19)=285 Σxy= 20+18+0+4+28=70 3(Σxy)= 3(70)=210 Reminder order of operations 1. Parentheses 2. squaring 3. multiplying and dividing 4. summation Σ 5. remaining addition and subtraction Now do the same for x = 4,5,7,8,12,10; y = 0,3,11,4,8,6 What about x = 1,22,4,0,6; y = 3,5,6,2,0? Use the above provided data to solve the following equations: Σx² - (Σx)²/n and Σy² - (Σy)²/n x y x² x-1 (x-1)² (x-3) xy y² y-1 (y-1)² (y-3) 4 0 16 3 9 1 0 0 4 1 -3 5 3 25 4 16 2 15 9 5 4 0 7 11 49 6 36 4 77 121 -1 100 8 8 4 64 4 49 5 32 16 3 9 1 12 8 144 11 121 9 96 64 3 49 5 10 6 100 9 81 7 60 36 3 25 3 Σ 398 40 312 28 280 246 26 188 14 Σx= 46 Σy= 32 Σx² = 16+25 …=398 Σy²= 246 (Σx)²= 46*46=2116 (Σy)²= (32)²=1024 Σx-1= 46-1=45 Σy-1=32-1=31 Σ(x-1)= 3+4+…=40 Σ(y-1)= -1+2+10+…=26 Σ(x-1)²= 9+16+36+…=312 Σ(y-1)²= 188 Σ(x-3)= 1+2+4+…=28 Σ(y-3)= 14 Σx/5 =46/5=9.2 Σy/5= 32/5=37.6 Σ(x-1)²/5= 312/5=62.4 Σ(y-1)²/5= 188/5=37.6 ΣxΣy= 46*32=1472 ΣxΣy/5= 1472/5=294.5 Σxy= 280 3(Σxy)= 3(280)=840 x y x² x-1 (x-1)² (x-3) xy y² y-1 (y-1)² (y-3) 1 3 1 0 0 -2 3 9 2 4 0 22 5 484 21 441 19 110 25 4 16 2 4 6 16 3 9 1 24 36 5 25 3 0 2 0 -1 1 -3 0 4 1 1 -1 6 0 36 5 25 3 0 0 -1 1 -3 Σ 33 16 537 28 476 18 137 74 11 47 1 Σx= 33 Σy= 16 Σx² = 537 Σy²= 74 (Σx)²= 33*33= 1089 (Σy)²= (16)²=256 Σx-1= 33-1=32 Σy-1=16-1=15 Σ(x-1)= 28 Σ(y-1)= 11 Σ(x-1)²= 476 Σ(y-1)²= 47 Σ(x-3)= 18 Σ(y-3)= 1 Σx/5 = 33/5=6.6 Σy/5= 16/5=3.2 Σ(x-1)²/5= 476/5=95.2 Σ(y-1)²/5= 47/5=9.4 ΣxΣy= 33*16=528 ΣxΣy/5= 528/5=105.6 Σxy= 137 3(Σxy)= 3(137)=411
