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Published on June 2, 2011

Author: gyanagnihotri

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statics: statics gyan agnihotri Positive and negative co-relation: Positive and negative co-relation Depending upon the direction of change of varietal correlation may be of two types. Positive Negative correlation Positive correlation: Positive correlation If both the variables are vary in same direction then correlation is said to be positive Negative correlation: Negative correlation If both the variables are vary in opposite direction then correlation is said to be negative. Simple and multiple correlation: Simple and multiple correlation Depending upon the study of variable correlation is of two types. simple: simple When only two variable are study then it is case of simple correlation. Multiple : Multiple When three are more variable are study then it is case of multiple study. Partial and total correlation: Partial and total correlation In case of partial correlation we are studying about 3 or more variable but consider only two variable which are effected to each other and the effect of other variable are neglected. Total multiple correlation : Total multiple correlation In case of total multiple correlation we are studying in 3 or more variable but not neglecting the effect of any other variable. Linear and non linear correlation : Linear and non linear correlation linear:- if the amount of the change in the above variable bears the constant ratio to the amount of change in another variable then the correlation is said to be linear. in such variable plotted on graph paper then all of the plotted point are often on straight line. Ex. x; 2 4 6 8 10 y. 5 10 15 20 25 Non linear : Non linear If the amount of change in one variable does not bears the constant ratio to the amount of change in another variable. Eg . production of a crop is variable R 1 3 2 – it means 2 is neglected R 1 2 3- multiple correlation R 3 1 2 – x3 x,x2 joint effect. Measure for the calculation correlation are: Measure for the calculation correlation are 1. graphical method :- standard diagram method 2.Numericl method:- -Karl Pearson correlation coefficient -spearmen's rank correlation coefficient - concurrent deviation method Karl Pearson correlation coefficient: Karl Pearson correlation coefficient Two measure the integrity of relation 2 variable x and y professor Karl Pearson. Which is denoted by x and y R=covariance of { x,y } The values of r is always lies is blue -1 to +1 covariance: covariance Covariance is the mean of deviation of x and y taken from their respective mean and it is define as follows. Slide 15: Covariance is not effected by change in origion but effected by change of scale and its value are always blue – ve to + ve that is the covariance may be positive negative and zero .the value of correlation is depend on value of correlation. Properties of karlpearson: Properties of karlpearson It is independent of change in origin and scale both. It is a pure no. and it is independent of unit of measurement. The limit of correlation are -1 to +1 The correlation coefficient is a geometric mean of both the regret ion coefficient Interpretation value of r: Interpretation value of r R=+1 perfect positive R=-1 perfect negative R=0 no correlation 0.75<r<1 high + ve correlation -0.75>r>0.5 avg – ve correlation +.5<r,0.75 moderately +correlation avg +correlation R<0.5 low level positive R>-0.5 low level - ve Assumption for karlpearson: Assumption for karlpearson The median relationship is found There is a cause and effect relation ship The two variable is effected to a great extent by a large number of independent so that they follow for a normal relation Merits of karl pearson: Merits of karl pearson The coefficient gives the relation direct as well as degree of relationship. Help to estimate the value of unknown variable with the help of known variable. limitation: limitation The assumption of linear relationship the variable may are may not be true. It is effected very much by the value of extreme value item It is a time taking Slide 21: The rank correlation coefficient given by sperman is – r= Where n=no of paired value d= rx - ry Slide 22: In case of repeated value then the adjusted correlation coefficient is- Feature of spearman rank: Feature of spearman rank It is based on rank only it is not base of actual. It is distribution free method Also known as non parometric method Sum of difference between of rank blue 2 variable should be= o Merits of rank correlation: Merits of rank correlation It is easy to understand and apply cmpare to karl pearson It is only method there rank is given and not the actual value Only method for analysis of qualitative data Limitation of rank correlation: Limitation of rank correlation It unsuitable for grouped data If the no of data is more than 30 then it is difficult to calculate Slide 26: Cocurrent deviation method is based on the direction of change in 2 paired variable it is calculated by- Merits and limitation: Merits and limitation Merits: -simple to understand - if no of observation is large then it is very suitable Limitation- it does not differentiate between small and big change. The result obtain by this method are only apprprimate indicator of presence or absence of of correlation Scattered diagram method : Scattered diagram method The only non numerical method to measure the correlation is scattered diagram method that is graphical method .this method shows a diagram of dotts which is known as scattered method. Merits and limitation: Merits and limitation Merit:-it is simple and non mathematical method. It is not effected by size and extreme item Limitation:-very rough measurement due to not known of exact magnitude. Slide 30: For the testing of significance of karl pearson we use the probable error which is .6745time of standard eroor . In probable eroor of correlation coefficient is on amount which is added to and standard from the value of r gives the upper and lower limit within which coefficient of correlation in population can be expected= r+pe {r}upper limit r- pe {r}lower limit r- pe < r+pe It is used to determine the reliability of value of r and its interpretations done as follows Slide 31: If mode value of r<6 pe {r} then r is not significant. If mode value is r>6pe{r} then r is high significant R2 is known as coefficient of determination and 1-r2 is known coefficient of non determination o<r2+1 1-r2 is known as coefficient of alienation which is used is standard eroor . Diff.between correlation and regration : Diff.between correlation and regration correlation Measure degree and direction of relationship between two variable. It is relative measure showing association of variables. Independent both change of orogin and scale. It is independent of unit measurement it is unit less measurement It is not forecasting method rgration It measure the nature of extend of avg relationship between two are more variable in term of the orig inal mean of data. It is absolute measurement of relationship It is independent of change of origin but not of change of scale. It is not independent of unit measurement. It is forecasting method Slide 33: There are two regretion line; 1.Regret ion line of y on x y = a+bx 2.regretion line of x and y x= a+by Properties of regretion cofficient: Properties of regretion cofficient The geometric mean of both the regretion cofficient is equal to correlation efficient. Sign of both regretion cofficient is same If any of regret ion coefficient is is greater than one then other must be less than one The arithmatic mean of both is always equal to or greater then correlation cofficient . It is independent of change of origin but not of scale They are also known as slop regretion line Both regretion line must be intersect each other at the point x and y there fore the mean of both the variable are known as point of intersection . If correlation cofficient is 0 then both regretion is also 0 If constant are known i.e.x,y,z,then equation of regretion line can be given. thanks: thanks

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