MATHS

thanx pritish and soumik....[1]

Regression lines are generally used for prediction purposes.

The regression line is generally taken to be of the form Y_t=a+bx_t - where a and b are constants that are to be determined.

Now Y_t is the actual value of a particular variable at the end of 't' yrs, whereas a+bx_t is da predicted value of da same.

The basic principle for determination of constants a and b is - Principle of least squares.

This principle says that the constants 'a' and 'b' are to be so determined such dat (Y_t-\left\{a+bx_t \right\} )^2 is minimum.

Now this eqn is partially differentiated w.r.t to a and b, to obtain 2 equations, called Normal equations.

These equations are then solved and a and b are determined, to get the regression coefficients.

However all this is only for ur personnel interest, without keeping in mind exam syllabus.

Yeah even I tried that. Most probably something wrong in the question. They must be asking for b².

okay thanks a lot pritish...

but one more doubt....

using these formulae,the ans to the q given by sridhar comes out to be -0.86?????

so the x bar and y bar..will be provided to us...and v hav to just put it in th formulae...???

The formulae to be used are pinked and above post #9 :P
If asked about regression coefficients, the slope of the regression line gives you that!

BITSAT mein aata hai yeh
pata nahi kahan ka hai yeh

Actually questions on BITSAT about this portion of statistics are mainly theoretical, so you needn't bother. The main calculative part comes on the properties of those b's.
Nobody's gonna ask you what's a regression..lol
But since you wanted to know, regressions are there in higher statistics.
http://en.wikipedia.org/wiki/Regression_analysis for more info. But all this went over my head, and it will for you too...
http://en.wikipedia.org/wiki/Linear_regression_model this is for lines of regression.

From Statistics chapter in BITSAT Arihant -:

Correlation : When two variables x and y are so related that a change in one is accompanied by a change in the other(increase or decrease), the variables are said to be correlated.

Positive(Direct) & Negative(Inverse) Correlation : When an increase(or decrease) in one variate corresponds to an increase(or decrease) in the other, the correlation is said to be positive/direct. It is negative when increase in one corresponds to decrease in the other or vice versa.

Karl Pearson's Coefficients of Correlation : The coefficients of correlation r between two variables x and y is defined by the relation

r = \frac {\sum{(x - \bar{x})(y - \bar{y})}}{n\sigma _{x} . n\sigma _{y}}

where x bar and y bar are the means of x and y(???) and sigma x and sigma y are their standard deviations.

Regression Lines -:
(a) Regression line of y on x is

y - \bar{y} = r\frac{\sigma _{y}}{\sigma _{x}}(x - \bar{x})

where r\frac{\sigma _{y}}{\sigma _{x}} = b_yx = regression coefficient of y on x.

(b) Regression line of x on y is

x - \bar{x} = r\frac{\sigma _{x}}{\sigma _{y}}(y - \bar{y})

where r\frac{\sigma _{x}}{\sigma _{y}} = regression coefficient of x on y.

Coefficient of correlation and regression coefficients are given as -:
r² = b_xyb_yx
So r = √|b_xyb_yx| if b_xy > 0
Or r = -√|b_xyb_yx| if b_xy < 0

heyy...we get such things in bits maths???

nvr heard about these things

Another problem from bits maths

1)Regression coefficients are -1.5 and 0.5. The value of correlation coefficient is
Answer is -0.75

2) Angle between two regressive lines is
Answer is arctan (b_yx - 1/b_xy)/1 + b_yx/b_xy

ya..had read in C++ probably.
aEb =a*10^b
0.8642E02 means 0.8642*10⁰² =86.42
0.2562E02 means 0.2562*10⁰² =25.62
the result of the division is 3.373