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BASIC STATISTICS FOR NON COMMERCE STUDENTS by : DR. T.K. JAIN AFTERSCHO ☺ OL centre for social entrepreneurship sivakamu veterinary hospital road bikaner 334001 rajasthan, india [email_address] mobile : 91+9414430763
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Find geometric mean of 3,6,12 In order to find geometric mean, first multiply them together : 3*6*12 = 216 now find factors of 216: 2*2*2*3*3*3 thus we have 2 and 3 coming three times. We have 3 numbers so we will take up that factor which comes three times or triple root of 216 = 2*3 = 6 answer.
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Find harmonic mean of 4,6,10 In order to find harmonic mean, first use 1/4, 1/6 and 1/10, now add them : we get : (30+20+12)/120 = 62/120 now multiply it by 1/3 (as there are 3 numbers) : 62/360 now reverse it : 360/62 we get : 5.8 answer
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Find 2 regression equations from following data?
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STEPS IN REGRESSION Basic equation : Y = A + BX XY = AX+BX^2 in these equation, we have to find values of A and B. First of find out covariance and variance B = covariance / variance of x on the basis of B, find value of A.
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Steps in regression 1. find DX and DY – DX is difference in each value of X with reference to the average value in X and DY is difference of each value in Y from the average of Y. 2. Find DX^2, DY^2, DXDY. 3. the average of DX^2 is variance of X and average of DY^2 is variance of Y. Average of DXDY is covariance of X and Y. 4 divide covariance by variance of X we get B.
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solution.... Covariance in our example is : - .67 variance in our example : .67 thus B =-1 put the value of B in the first equation : Y = A + BX here Y (average of Y) = 3, and X = (average of X) = 3 thus : 3= A+(-1)*3, we get A = 6, thus our regression equation is ready.
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Given the regression equations : 3X+Y=13 and 2X+5Y=20, which is the regression equation of Y on X? First equation : Y = 13- 3X 2 nd equation : Y = 4-2/5X square roots of products of B should be between -1 and 1. so try : (-3 * -2/5) = (-) 1.20, its square root is : 1.09, so this is not possible. However, only 2 nd equation can be taken up as its value is .4 which is between -1 and 1.
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Given the following equation : 2x-3y = 10, 3x+4y=15, which is regression equation of X on Y? X = 5+3/2Y here B is 1.5 X = 5-4/3Y here B is -1.33 B should be between -1 and +1, so both the equations are not valid regression equations.
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Y on X is : Y =-2X+3 and that of X on Y is 8X=-Y+3, what is coefficient of correlation? B in the first equation is : -2 and in second equation is -1/8, now multiply them, we get : 1/4, which gives us ½ or .5 as answer. As both the values are negative, the answer should be -.05
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