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# CORRELATION AND REGRESSION

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Submitted by Coloratus on Fri, 2012-05-04 12:59
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## Complete answer to first problem

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Formula xxxx xxxxxxxxxx r xxx

As a result, xx have:

Submitted by rajendrabnk on Fri, 2012-05-04 15:43
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x have tried as much as possible to explain to xxx xxx xxxxxxxx Let xx know xx xxx xxxx xxxx xxxxx Also, Please DO NOT forget xx rate me xx you liked xx xxxxxxxx A testimonial xxxx be a xxxxx xxx xx acknowledge! xx

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17.2

The xxxxxxx xxx the xxxxxxxxxxx coefficient xx given xx

Now, all the xxxxxx xxx xxxxx in the xxxxxxxxx Substituting, xx get:

r = xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxx xxxx

2 )]

r = xxxxxxxxxxxxxxxxxxx

x = 0.7835

17.3

xxx xxxxxxxxxxx xxxxxxxxxxxx represents xxx xxxxxx of xxxxxxxxxxx xx xxxxxxxxxx xxxxxxxxx xx xxx variable

explained xx the xxxxx xxxxxxxxx xxxxx 78.35% xx variation xx Y is explaned by X.

Section B

1. The xxxxxxx numbers xxxx xxxx filled.

xx Y is perfectly correlated with X. In xxxx xxxxx for xxxxx additional x, x xxxxxxx by xx xxx

values xxx xxxxxxxxxx xxxxxxxxxxxx

x Y

x 7

2 xx

x xx

10 52

13 67

b) x xx xxxxxxxxx negatively correlated xxxx X. xxxx means xxxx for xxxxx xxxxxxxxxx xx x xxxxx xx

xxxxxxxx xxxxxxxxx xx x xxxxxxxxxx xxxxx amount (Here, x xxxx xxxxx xx

x x

1 5

x x

x 3

x 2

x x

c) The mean xxxxxx be xxxx xxx standard xxxxxxxxx should xx

- - - more text follows - - -

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# data

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 Year x y Motorboats xxxxxxxxxx xxxxxxx xxxxxx xy x square x xxxxxx 1977 xxx 13 xxxx xxxxxx 169 xxxx xxx xx xxxx xxxxxx 441 1979 xxx 24 11544 xxxxxx xxx xxxx 498 xx 7968 xxxxxx 256 xxxx 513 xx xxxxx 263169 576 1982 512 20 xxxxx xxxxxx xxx xxxx xxx 15 7890 xxxxxx 225 1984 559 34 xxxxx xxxxxx 1156 xxxx 585 33 xxxxx xxxxxx xxxx xxxx xxx 33 xxxxx 376996 xxxx 1987 xxx 39 25155 xxxxxx 1521 1988 xxx 43 xxxxx xxxxxx xxxx xxxx 711 xx 35550 505521 xxxx 1990 719 47 xxxxx xxxxxx 2209 xxx xxxx xxx 412 xxxx xxxxxx Ʃ(x^2) 4618597 Ʃ(y^2) 14056 r xxxxxxxxxxxx

# Regression line

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 xxxxxxx OUTPUT Regression xxxxxxxxxx Multiple R 0.9414772888 R Square xxxxxxxxxxxx Adjusted x xxxxxx 0.8769111091 Standard Error xxxxxxxxxxxx xxxxxxxxxxxx 14 ANOVA df SS xx x xxxxxxxxxxxx F Regression x 1711.9786630483 xxxxxxxxxxxxxxx xxxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxx 12 xxxxxxxxxxxxxx xxxxxxxxxxxx xxxxx xx xxxxxxxxxxxxxxx xxxxxxxxxxxx xxxxxxxx xxxxx t xxxx xxxxxxx xxxxx 95% xxxxx 95% Lower xxxxx Upper xxxxx Intercept -41.4304389485 7.4122172282 -5.5894798645 xxxxxxxxxxxx xxxxxxxxxxxxxx -25.2806049554 xxxxxxxxxxxxxx -25.2806049554 x xxxxxxxx 1 xxxxxxxxxxxx 0.0129049736 9.6754705394 0.0000005109 xxxxxxxxxxxx 0.1529792144 0.0967441702 0.1529792144 For xxx boats, x x xxxxxxxxxxxxx Confidence interval xx xxx confidence xxxxx xxxxxxxxxxxxx to 69.4627304557

# xxxxxx

x

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xxx

The xxxxxxxxxx xxxxxxxxxxxx xx calculated by the following equation (In xxxxxx x put xx this formula

and xx calculates xx xxxxxxx xx xx just like x calculator).

xxxx xxx xxxxxxxxxxx coefficient xxxxx xxxxx of 0.941 xxxxx xxx xxx predict xxx xxxx score from

the xxxxxx xxx xxxx xxx error xx prediction xx xxxxxxxxxx small. We xxxxx conclude that this xxxx

is reliable.

xxx xxxxxxxxxx xxxxxxxx is xxxxxxxxx below xxx xx is xxxxxxxx xx x similar xxxxxxx to xxx

correlation coefficient. xxx xxxxxxxxxx equation is xxxx xx xxxxxxx xxxxxx xx xxx xxxxxxxxx

xxxxx (Y) from xxxxxx of xxx Independent Value (X). The xxxxxxx x and I xxxxx xxx the xxxxx and

xxxxxxxxx respectively.

xxx slope and intercept xxx xxxxxxxx using the xxx xxxxxxxxx below.

You can either calculate xxx above xxxxxxxx by xxxxxxxxxx or by xxxxx (I had xxxx xxxxxxxxxx xx

xxxxxxx All the values that are xxxxxx xxx calculation xx Slope and x are in excel. You xxx just xxx

in xxx xxxxxx xxx

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Submitted by shahimermaid on Fri, 2012-05-04 14:10
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## the answer is in attached file

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xxxx

xxxxxxxxxxxxxx x xxxxx - xxxxxxxxxx x Sqrt([NΣX2 x xxxxxxx xxxx [NΣY2 x (ΣY)2])

= 10 (5980)-(525)(100)/ sqrt ({10(32,085)-(525)^2} Sqrt xxx xxxxxxxxxxxxxxxx

x 59800 -52500/ sqrt ({320850-275625} xxxx xxxxxxxxxxxxxx

xxxxxxxxxx (45225) Sqrt xxxxxx

=7300/212.66 x 43.82

xxxxx

xxxx

r^2 xxx be interpreted xx the xxxxxxxxxx of variance xx y xxxx is accounted xxx by x. r^2 = xxxx xx xxx xxxx 61 xxxxxxxxxx of the xxxxxxxx in y xx xxxxxxxxx xxx xx xxxxxxxxxxx xx xx

section x

Q1 a) missing y= xx

b) y x xxxxxxxxx

c) xx 2,3,4,5,6

y: xxxxxxxxx

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
 x y x^2 xxx xy xxx xx xxxxxx 169 5811 xxx 21 211600 441 xxxx xxx xx 231361 576 xxxxx 498 xx 248004 xxx 7968 xxx 24 263169 xxx 12312 xxx 20 xxxxxx 400 10240 xxx xx xxxxxx 225 7890 559 xx xxxxxx xxxx xxxxx xxx xx 342225 xxxx 19305 614 33 xxxxxx xxxx 20262 645 39 xxxxxx 1521 xxxxx 675 xx xxxxxx 1849 xxxxx 711 50 505521 xxxx 35550 xxx xx xxxxxx xxxx xxxxx xxxx 412 xxxxxxx xxxxx xxxxxx

Q2 Correlation(r) = NΣXY - xxxxxxxxxx / xxxxxxxxxxx - (ΣX)2] Sqrt xxxxxx x xxxxxxxx

14 (247521)-(7945)(412)/ xxxx xxxxxxxxxxxxxxxxxxxxxx sqrt x 14(14056)-(412)^2

3465294-3273340/ sqrt (14(4618597)-(7945)^2) xxxx ( xxxxxxxxxxxxxxxxx

xxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xxxxxxxxxxxxxx x 164.44

xxxxx

xx is xxxxxxxxxx correlated

xx

Simple xxxxxx xxxxxxxxxx xxxxxxxx Dependent Variable: y Independent xxxxxxxxx x

Regression xxxxxxxxxxx = x + xx Slope(b) = (NΣXY x (ΣX)(ΣY)) / xxxxxx x xxxxxxxxxxxxxxxxxxxx = (ΣY x xxxxxxx x N

Y=-41.43 +0.12 xxxxxxx xx xx 140

c) R-sq x 0.8863795 . xxx accuracy is xxxx

Submitted by shahimermaid on Fri, 2012-05-04 09:13
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## solution to section A

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17.2

Correlation(r) = NΣXY - (ΣX)(ΣY) / xxxxxxxxxxx x (ΣX)2] xxxx xxxxxx - (ΣY)2])

x 10 xxxxxxxxxxxxxxxxxx xxxx ({10(32,085)-(525)^2} xxxx xxx (1192)-(100)^2})

x xxxxx -52500/ xxxx ({320850-275625} xxxx {11920-10000})

=7300/sqrt xxxxxxx Sqrt xxxxxx

xxxxxxxxxxxx x xxxxx

xxxxx

17.3

xxx xxx be xxxxxxxxxxx xx xxx percentage of xxxxxxxx xx y that is accounted for by xx xxx x xxxx xx say that 61 percentage xx the xxxxxxxx xx x xx accounted xxx by differences in xx