13 vi 1 CI for paired difference n S n t d d 1 2 C ANOVA i One way N y y SS

# 13 vi 1 ci for paired difference n s n t d d 1 2 c

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13 vi) % ) 1 ( CI for paired difference n S n t d d 1 , 2 C) ANOVA i) One-way N y y SS Total 2 2 N y n T SS i i Trt 2 2 SSE SS SS Trt Total Alternatively: ) ( 1 1 x x n SStrt i K i where x is the grand mean ii) Two-way SSB SStrt SSE SStotal N y n B SSB i i 2 2
14 D) Time Series and Index Numbers i) b =   2 2 n x x n y x xy The slope of the regression line x b y a The intercept bx a y ˆ Least squares regression line Product moment correlation coefficient   2 2 2 2 y y n x x n y x xy n r Spearman’s rank correlation coefficient ) 1 ( 6 1 2 2 n n d r iii) )% 1 ( Prediction interval for the individual and mean values respectively ) var( 1 ˆ ) var( 1 1 ˆ ; )% 1 ( 2 / 2 , 2 / 2 / 2 , 2 / x x x n S t y x x x n S t y PI p y x n p y x n Note that mse S y x /
15 E) Probability Distributions i) Binomial Probability Distribution: x n x n x q P C x X P ) ( where n x ..., 2 , 1 , 0 np X E ) ( , npq x 2 ii) Poisson Probability Distribution: ) ( x X P = ! x e x , where x = 0, 1, 2 . . . ) ( X E , and ) ( X Var ii) Exponential Probability Distribution 0 , ) ( x e x X f x a e a x P ) ( , 1 ) ( X E , 2 1 ) ( X Var iii) Uniform Probability Distribution
16 , 2 ) ( b a X E 12 ) ( ) ( 2 a b X Var iv) Laspeyre’s price index = 100 1 o o o q P q P Paasche’s price index = 100 1 1 1 q P q P o v) Weighted index 100 0 1 w p p w where w are weights and 0 1 p p are price relatives. F) Chi-Squared e e o c 2 2 ) ( where o is the observed frequency where e is expected frequency.
17 G) PROBABILITY: The Bayesian Theorem n i i i i B P A B B P A B P B A P ) ( / ) ( ) / ( ) / ( Where B is an event common to the events i A , n i , , 1 . H) Exponential Smoothing New forecasted value = Old forecasted value + (Actual Value Old forecasted Value) Or t t t i F X F F 1 where is the smoothing constant (between 0 and 1), i X = Actual value in i the period, 1 i F Forecasted value in i th period.

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• Fall '18
• F. TAILOKA
• Normal Distribution, credit manager, SCHOOL OF GRADUATE STUDIES, Copperbelt University, Mr. Mumba
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