MATHS

thank u pritish

i kind of a bit understand the second one..i mean the starting....

if u could jus provide me a few simple formulae..that could b used...

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.

Don't worry. In exam questions will be correct and answers will match. [1]

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

Look at it like usual straight line geometry. xbar and ybar are coordinates of a point which satisfy the regression line. x and y are any arbitrary point on the line. Using the slope form of the line, the regression coefficient is the slope of the line.
Usually you'll be given the line and you have to find b. But it's better to know actually what the terms stand for.

For the Karl Pearson formula, you'll be given almost all values and will have to find one of them from the equation.

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!

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.

is there anyone on tiit who could explain me a little about this bloody damn thing called regression?????.......i searched the sites...but could understand nothing more than...what a regressive line means????????

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