Least Squares Regression

**Apache** · August 18th 2009, 06:27 AM

I'll be honest i've not got much idea on where to start with this, could anyone point me in the right direction ?

A sample of data from 40 households in a particular area in 2007 yielded the following information, where X is disposeable income per head and Y is disposeable expenditure per head.

$\sum X_i = 200$ $\sum Y_i= 160$

$\sum X_iY_i=875$ $\sum X$ $^{2}_i =1100$

$\sum (Y_i - \bar{Y})^{2} = 75.25$

a) Show that in the relationship $Y_i = \alpha +\beta X_i + u_i$

where $u_i$ is the disturbance term, the least squares regression estimates of $\alpha, \beta$ are 0.25 and 0.75 respectively.

**CaptainBlack** · August 18th 2009, 09:46 PM

Originally Posted by Apache

I'll be honest i've not got much idea on where to start with this, could anyone point me in the right direction ?

A sample of data from 40 households in a particular area in 2007 yielded the following information, where X is disposeable income per head and Y is disposeable expenditure per head.

$\sum X_i = 200$ $\sum Y_i= 160$

$\sum X_iY_i=875$ $\sum X$ $^{2}_i =1100$

$\sum (Y_i - \bar{Y})^{2} = 75.25$

a) Show that in the relationship $Y_i = \alpha +\beta X_i + u_i$

where $u_i$ is the disturbance term, the least squares regression estimates of $\alpha, \beta$ are 0.25 and 0.75 respectively.

See here

CB

**Apache** · August 20th 2009, 05:18 AM

Thanks for that think ive cracked it,

$b= \frac {40 * 875 - 200 * 160} {40 * 1100 - 200^2}$

= 0.75

$a = 4 - 0.75 * 5$

= 0.25

The next part of my question asks to give interpretations of $\alpha$ and $\beta$ and discuss wether the signs on the sample estimates accord with your expectations?

Is this referring to the figures of 0.25 and 0.75 and wouldnt they always be positive ?

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