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Correlations

Test if the variables are significantly correlated

Copy data to SPSS(as is). Run correlation analysis. It will result in a correlation matri.

!ith " #$ significant

%naly&e #$ correlate #$ bivariate

%ll data are scale. Put all into variables. Chec' pearsons.

Correlations

weight height grademath allowance circumference

weight Pearson Correlation 1 .516** .163 -.408* .9**

!ig. "-tailed# .003 .389 .05 .000

$ 30 30 30 30 30

height Pearson Correlation .516** 1 -.14 -.99 .361*

!ig. "-tailed# .003 .51 .109 .050

$ 30 30 30 30 30

grademath Pearson Correlation .163 -.14 1 .049 .04

!ig. "-tailed# .389 .51 .%96 .80

$ 30 30 30 30 30

allowance Pearson Correlation -.408* -.99 .049 1 -.33

!ig. "-tailed# .05 .109 .%96 .08

$ 30 30 30 30 30

circumference Pearson Correlation .9** .361* .04 -.33 1

!ig. "-tailed# .000 .050 .80 .08

$ 30 30 30 30 30

**. Correlation is significant at the 0.01 le&el "-tailed#.

*. Correlation is significant at the 0.05 le&el "-tailed#.

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$egati&e relationshi' -( indirect relationshi'

)f it is far from 1 it is not related or ma+ ha&e relationshi' ,ut wea

Which of the quantitative variables are significantly correlated?

eight and height

/o ' 0 2here is no linear relationshi'

/a ' 0 2here is a linear relationshi'

  .01

P&alue .003 r.516

ecision e7ect /o

Conclusion 2here is a significant linear relationshi'

eight and grade

/o ' 0

/a ' 0

  3.01

P&alue.389

ecision ail to e7ect /o

Conclusion 2here is no linear relationshi' ,etween weight and grade

Scatter plot

raphs #$ *egacy +ialogs #$ Scatter

Regression

To test R,oth values are scale

Response variable- ,P

Correlate #$ ,ivariate. Chec' persons two tailed.

o- p / 0 There is no linear relationship between sodium and ,P

a- p 1 0 There is a linear relationship between sodium and ,P

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2 / .03

Correlations

!odium P

!odium Pearson Correlation 1 .94**

!ig. "-tailed# .000

$ 1 1

P Pearson Correlation .94** 1

!ig. "-tailed# .000

$ 1 1

**. Correlation is significant at the 0.01 le&el "-tailed#.

P value 4 .003

+ecision- Re5ect o

Conclusion- There is a linear relationship between 6a and ,P

ighly significant

R- .789

*inear Regression

%naly&e #$ Regression #$ *inear

,p : dependent

6a : independent

Variables Entered/Removedb

:odel

;aria,les

<ntered

;aria,les

emo&ed :ethod

1 !odiuma . <nter 

a. =ll re>uested &aria,les entered.

,. e'endent ;aria,le P

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Model Summary

:odel !>uare

 =d7usted

!>uare

!td. <rror of the

<stimate

1 .94a .888 .8%% 6.833

a. Predictors "Constant# !odium

Rs;uare #$ coefficient of determination< variation

A!VAb

:odel !um of !>uares df :ean !>uare !ig.

1 egression 3136.8%% 1 3136.8%% %9.45% .000a

esidual 394.%89 10 39.4%9

2otal 3531.66% 11

a. Predictors "Constant# !odium

,. e'endent ;aria,le P

This table will give P value

Testing the significance of ,eta

o- , / 0

a- , 1 0

2- .03

P value 4 .003

+ecision- Re5ect o

Conclusion- There is a regression e;uation

If fail to re5ect o< no need for table =. 6o e;uation.

Regression e;uation / found on last table >coefficients?

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Coefficientsa

:odel

?nstandardi@ed Coefficients

!tandardi@ed

Coefficients

t !ig. !td. <rror eta

1 "Constant# -198.06 41.33 -4.803 .001

!odium 5.456 5.885 .94 8.914 .000

a. e'endent ;aria,le P

REGRESSION EQUATION:

@bp / #37A.09B D9.8DBEna

  y#int slope

If sig is 0< pvalue is significant for slope

Predict a persons ,P when his sodium is a. B.= and b. F.B mg

Simply substitute in the e;uation for E

Multiple regression

%naly&e #$ Regression #$ *inear Regression

S,P : dependent

Cd< Ginc : Independent

Model Summary

:odel !>uare

 =d7usted

!>uare

!td. <rror of the

<stimate

1 .441a .194 .048 4.608%

a. Predictors "Constant# C Ainc

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A!VAb

:odel !um of !>uares df :ean !>uare !ig.

1 egression 1608.3 804.116 1.38 .304a

esidual 6661.48 11 605.589

2otal 869.%14 13

a. Predictors "Constant# C Ainc

,. e'endent ;aria,le !P

 No linear regression/ relationship.

Correlations

C Ainc !P

C Pearson Correlation 1 .931** .439

!ig. "-tailed# .000 .116

$ 14 14 14

Ainc Pearson Correlation .931** 1 .44

!ig. "-tailed# .000 .131

$ 14 14 14

!P Pearson Correlation .439 .44 1

!ig. "-tailed# .116 .131

$ 14 14 14

**. Correlation is significant at the 0.01 le&el "-tailed#.

Ginc and Cd are highly correlated

% linear regression for the two can be done with &inc as dependent

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Coefficientsa

:odel

?nstandardi@ed Coefficients

!tandardi@ed

Coefficients

t !ig. !td. <rror eta

1 "Constant# -5.515 13.6% -.416 .685

C 1.936 .19 .931 8.81 .000

a. e'endent ;aria,le Ainc

@ intercept is no significant so constant is not added to the regression e;uation

R value/ .7=3 strong linear relationship