Amit Sir Please Help

[vandita24x7]

                   

[Dreyfus]

Although this post is reserved for Amit sir's reply.....but I eagerly wanted to try this one.....I am getting alpha hat as 3 please confirm if it is right or wrong....

[vandita24x7]

Vaibhav dnt knw the answer...if ur pretty sure..show the working

vandita

On 13 Apr 2014 14:49, "Vaibhav Garg [via Discussion forum]" <[hidden email]> wrote:

Although this post is reserved for Amit sir's reply.....but I eagerly wanted to try this one.....I am getting alpha hat as 3 please confirm if it is right or wrong....

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[Dreyfus]

OK...I proceeded this way..... I first computed the mean of X which turns out to 0 and mean of Y which turns out to 3
Since sample regression line passes through sample means therefore
Mean of y= alpha cap + beta cap*mean of x
3= alpha cap + beta cap*0
Alpha cap=3...

[Arushi :))]

I am also getting alpha as 3.
For beta, i think answer should be not enough info is provided . because we can't find out the individual values of y from whatever is given.

[Amit Goyal]

For Q 20 it is (b) Slope estimate is 1
For Q 21 it is (c) Intercept estimate is 3
For Q 22 it is (b) R-square is strictly above 0

[Akshay Jain]

and
the slope coefficient is not 0 therefore R^2>0

[Shefali]

Which book should i refer for etx...basic etx...or essential etx???

[Akshay Jain]

Basic ecotrix....

[Shefali]

OH Thanxx ya.
I have essentials of etx...wht do i do?Do i really need to get basic etx?
Eseentials wont do?
Ah ..Please suggest :(

[Akshay Jain]

I have not read the essentials 1 so cant really tel but max pple say that the contents of both are more or less the same....

[Amit Goyal]

Hi Akshay,

There is a mistake in your analysis. We are not given E(Y|X=1) and E(Y|X=-1) . These are population averages. We are only given sample averages. If the observations are (-1, y(1)), (-1, y(2)), (-1, y(3)), (1, y(4)), (1, y(5)), (1, y(6)), we only know that [y(1) + y(2) + y(3)]/3 = 2 and  [y(4) + y(5) + y(6)]/3 = 4.

Note that x-bar = 0. Thus, least square estimate of the slope coefficient is:
b = [x(1)y(1) + x(2)y(2) + x(3)y(3) + x(4)y(4) + x(5)y(5) + x(6)y(6)]/ [x(1)^2 + x(2)^2 + x(3)^2 + x(4)^2 + x(5)^2 + x(6)^2]
= [-y(1) -y(2) -y(3) + y(4) + y(5) + y(6)]/ [6]
= [-6 + 12]/6
= 1

The estimate of the intercept coefficient is
a = (y-bar) - b (x-bar) = y-bar = [y(1) + y(2) + y(3) + y(4) + y(5) + y(6)]/6 = [6 + 12]/6 = 3.
 

[vandita24x7]

Thanks a lot sir..!

vandita

On 14 Apr 2014 07:57, "Amit Goyal [via Discussion forum]" <[hidden email]> wrote:

Hi Akshay,

There is a mistake in your analysis. We are not given E(Y|X=1) and E(Y|X=-1) . These are population averages. We are only given sample averages. If the observations are (-1, y(1)), (-1, y(2)), (-1, y(3)), (1, y(4)), (1, y(5)), (1, y(6)), we only know that y(1) + y(2) + y(3)/3 = 2 and  y(4) + y(5) + y(6)/3 = 4.

Note that x-bar = 0. Thus, least square estimate of the slope coefficient is:
b = [x(1)y(1) + x(2)y(2) + x(3)y(3) + x(4)y(4) + x(5)y(5) + x(6)y(6)]/ [x(1)^2 + x(2)^2 + x(3)^2 + x(4)^2 + x(5)^2 + x(6)^2]
= [-y(1) -y(2) -y(3) + y(4) + y(5) + y(6)]/ [6]
= [-6 + 12]/6
= 1

The intercept coefficient is
a = (y-bar) - b (x-bar) = y-bar = [y(1) + y(2) + y(3) + y(4) + y(5) + y(6)]/6 = [6 + 12]/6 = 3.
 

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[Akshay Jain]

Thanku sir for pointing out.....i forgot to distinguish b/w sample reg lne and population reg line
right answers but wrong approach...