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Q1: Using regression techniques, we can plot a scatter diagram and plot a line to the data using the Least Squares method. Generally, the points do not fall directly on the line. Why does this happen? Is it a problem? Explain the parameters in a linear regression line with the aid of co-ordinate axis. How could you say, if the slope is negative, positive, or zero just by looking at the plotted data [Hint: using the independent and dependent relationship]?

Q2: The t statistic and the partial F statistic are, closely related. Explain this relationship. Which would you prefer to use?

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1. If all the points lie exactly on the regression line, then we get a corelation coefficient of +1 or -1 (depending upon the nature of the relationship between the variables). But in most cases corelation coefficients vary significantly from these ideal ...

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Sufficiency and Order Statistics

Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the uniform distribution over the closed interval [-theta, theta ]
having pdf f(x; theta ) = (1/2(theta))I[-theta , theta ](x).

Argue that the mle of theta; equals theta;hat= max(-Y1, Yn).
Demonstrate that the mle theta;hat is a sufficient statistic for theta;.
Define at least two ancillary statistics for this distribution

See attachment for better symbol representation.

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