CORRELATION AND REGRESSION
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Formula that xxxxxxxxxx x xxx
As a result, xx have:
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x have xxxxx as much as possible xx explain to xxx xxx xxxxxxxx xxx me xxxx xx you need more xxxxx Also, Please DO xxx xxxxxx to rate me xx xxx xxxxx my xxxxxxxx A testimonial xxxx be x xxxxx xxx xx acknowledge! :)
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xxxx
xxx xxxxxxx xxx xxx correlation xxxxxxxxxxx is given xx
Now, all xxx xxxxxx xxx xxxxx in the xxxxxxxxx Substituting, xx get:
x x [10(5980)(525*100)]/[sqrt((10*32085)525 2 xxxxxxxxxxxxxxxxx 100
x xx
x = 7300/(212.66*43.81)
r x xxxxxx
xxxx
The correlation coefficient represents the xxxxxx xx xxxxxxxxxxx of variation) xxxxxxxxx xx xxx xxxxxxxx
explained xx xxx xxxxx variable. xxxxx xxxxxx xx xxxxxxxxx in Y xx explaned xx xx
Section B
xx xxx xxxxxxx numbers xxxx been filled.
xx Y is xxxxxxxxx xxxxxxxxxx with X. xx xxxx xxxxx xxx every xxxxxxxxxx x, x xxxxxxx by 5. xxx
xxxxxx xxx calculated accordingly.
x Y
x x
x xx
x xx
xx 52
xx 67
b) Y is xxxxxxxxx negatively correlated xxxx X. This xxxxx that
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data
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx  x  x  
Motorboats xxxxxxxxxx  Manatee deaths  xy  x square  y xxxxxx  
1977  447  xx  5811  199809  xxx 
xxxx  460  xx  xxxx  xxxxxx  441 
xxxx  481  24  xxxxx  231361  576 
1980  xxx  xx  xxxx  xxxxxx  xxx 
1981  xxx  xx  xxxxx  263169  xxx 
xxxx  512  xx  xxxxx  xxxxxx  xxx 
xxxx  526  xx  7890  xxxxxx  225 
1984  xxx  xx  xxxxx  xxxxxx  1156 
1985  xxx  33  xxxxx  xxxxxx  1089 
xxxx  xxx  xx  xxxxx  xxxxxx  1089 
1987  645  xx  xxxxx  xxxxxx  xxxx 
1988  xxx  43  29025  xxxxxx  1849 
1989  xxx  50  xxxxx  505521  2500 
xxxx  719  xx  33793  xxxxxx  xxxx 
xxx  xxxx  
Ʃy  412  
xxxx  xxxxxx  
xxxxxxx  xxxxxxx  
Ʃ(y^2)  xxxxx  
r  0.9414772888 
xxxxxxxxxx line
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx OUTPUT  
Regression Statistics  
xxxxxxxx x  xxxxxxxxxxxx  
x Square  0.8863794853  
Adjusted x Square  0.8769111091  
xxxxxxxx Error  xxxxxxxxxxxx  
Observations  14  
xxxxx  
df  SS  xx  x  xxxxxxxxxxxx F  
Regression  1  1711.9786630483  1711.9786630483  93.6147301596  xxxxxxxxxxxx  
Residual  12  xxxxxxxxxxxxxx  18.287492365  
xxxxx  13  1931.4285714286  
xxxxxxxxxxxx  xxxxxxxx xxxxx  x xxxx  Pvalue  xxxxx xxx  xxxxx 95%  xxxxx 95.0%  Upper 95.0%  
Intercept  41.4304389485  7.4122172282  xxxxxxxxxxxxx  0.0001180993  57.5802729415  xxxxxxxxxxxxxx  xxxxxxxxxxxxxx  xxxxxxxxxxxxxx 
X xxxxxxxx x  0.1248616923  0.0129049736  9.6754705394  0.0000005109  0.0967441702  xxxxxxxxxxxx  xxxxxxxxxxxx  xxxxxxxxxxxx 
xxx 821 boats, x =  61.0810104252  
Confidence interval at 95% confidence xxxxx  xxxxxxxxxxxxx  xx  xxxxxxxxxxxxx 
Sheet3
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xxx
xxx xxxxxxxxxx coefficient xx calculated by xxx following xxxxxxxx (In xxxxxx I put in this xxxxxxx
and it calculates xx xxxxxxx xx xx xxxx xxxx a calculator).
Now, The correlation coefficient (rxy) xxxxx xx xxxxx means you xxx predict xxx xxxx xxxxx xxxx
xxx xxxxxx xxx xxxx the error xx xxxxxxxxxx is xxxxxxxxxx xxxxxx xx would xxxxxxxx that this test
is xxxxxxxxx
The regression equation is presented below xxx xx is xxxxxxxx in a xxxxxxx fashion to the
xxxxxxxxxxx coefficient. xxx xxxxxxxxxx xxxxxxxx xx used to xxxxxxx values xx the dependant
xxxxx xxx xxxx values of xxx Independent xxxxx (X). The xxxxxxx x and x stand xxx the xxxxx and
xxxxxxxxx xxxxxxxxxxxxx
xxx slope and xxxxxxxxx xxx xxxxxxxx xxxxx the two equations below.
xxx xxx
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xxxx
Correlation(r) = xxxxx x (ΣX)(ΣY) x xxxxxxxxxxx  xxxxxxx xxxx [NΣY2  (ΣY)2])
x 10 (5980)(525)(100)/ sqrt ({10(32,085)(525)^2} Sqrt {10 (1192)(100)^2})
= 59800 xxxxxxx sqrt ({320850275625} Sqrt xxxxxxxxxxxxxx
=7300/sqrt (45225) Sqrt xxxxxx
xxxxxxxxxxxx x xxxxx
=0.78
xxxx
r^2 xxx be xxxxxxxxxxx as xxx percentage xx xxxxxxxx xx y that xx xxxxxxxxx for by xx r^2 = 0.61 xx say xxxx 61 percentage of xxx variance xx y is xxxxxxxxx for xx xxxxxxxxxxx in x.
section B
Q1 xx xxxxxxx y= xx
b) x x 5,4,3,2,1
c) x: 2,3,4,5,6
xx xxxxxxxxx
xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx  y  x^2  xxx  xx 
xxx  13  xxxxxx  169  5811 
xxx  21  xxxxxx  441  xxxx 
xxx  xx  231361  xxx  xxxxx 
498  16  xxxxxx  256  7968 
513  xx  263169  576  12312 
xxx  xx  xxxxxx  400  xxxxx 
526  xx  276676  xxx  xxxx 
xxx  xx  312481  xxxx  19006 
xxx  33  xxxxxx  xxxx  xxxxx 
xxx  33  xxxxxx  1089  20262 
645  xx  416025  1521  25155 
xxx  xx  xxxxxx  1849  xxxxx 
xxx  50  505521  xxxx  35550 
xxx  xx  516961  2209  xxxxx 





7945  412  xxxxxxx  14056  xxxxxx 
Q2 xxxxxxxxxxxxxx = xxxxx x xxxxxxxxxx x Sqrt([NΣX2 x (ΣX)2] xxxx xxxxxx  xxxxxxxx
xx xxxxxxxxxxxxxxxxxxxxx xxxx xxxxxxxxxxxxxxxxxxxxxx sqrt ( xxxxxxxxxxxxxxxxx
34652943273340/ xxxx xxxxxxxxxxxxxxxxxxxxxx xxxx x xxxxxxxxxxxxxxxxx
191954/sqrt(
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solution to section A
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17.2
Correlation(r) x xxxxx  (ΣX)(ΣY) x Sqrt([NΣX2 x (ΣX)2] xxxx xxxxxx x (ΣY)2])
= 10 xxxxxxxxxxxxxxxxxx xxxx ({10(32,085)(525)^2} xxxx xxx (1192)(100)^2})
x 59800 xxxxxxx sqrt xxxxxxxxxxxxxxxx xxxx {1192010000})
=7300/sqrt (45225) Sqrt xxxxxx
=7300/212.66 x xxxxx
xxxxx
17.3
r^2 can be xxxxxxxxxxx xx xxx percentage of variance in x that xx accounted xxx by xx xxx x 0.61 xx xxx xxxx xx percentage of the xxxxxxxx in x xx accounted for xx differences in xx
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