Explore a comprehensive tutorial on linear regression and correlation coefficient, complete with solved examples. Delve into key concepts including correlation ranges, covariance of dependent variables, and the properties of correlation coefficients. Learn how to calculate Spearman's rank correlation coefficient and apply the method of least squares to find regression equations. Examine the relationship between variables, predict outcomes, and understand the mathematical proofs behind correlation and regression principles. Gain practical skills in statistical analysis through various solved problems and past exam questions.
Overview
Syllabus
Correlation lies b/w -1 and +1.
Q 1.20 Book Statistical Methods by Prof. shahid Jamal (for B.sc and B.A).
(Q 1.24 Book Statistical Method by prof.shahid jamal)B.sc 2 paper 4..
Two indep. variates X1 and X2 have means 5 and 10 and variances 4,9.find corr. coef. b/w y1 and y2.
Covariance of two random variables when X and Y are dependent variables. cov(x,y)=E(x y) - E(x).E(y).
corr b/w x and y is "r".show that corr b/w ax and by is +r or -r acc to a and b hv same or diff sign.
Proof (Variance of the sum or difference of the two random variables.) var(x+y)=v(x)+v(y)+2cov(x,y).
Show that Coefficient of correlation is independent of change of Origin and Scale..
Derivation of Spear man's rank correlation coeff.(Bsc past paper iv 2015,Q.8(a) 2010Q.9(a) 2009Q6(a).
Find regression equation for cost related to age.also predict the maintenance cost,if x=12.
Method of least square (how to find regression coefficient (b) and regression constant (a)..
Coefficient of Correlation is lie b/w -1 and +1to prove this property we standardized r.v's X and Y..
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Statistics is Fun A.H
