H7Q5 Sorry for the long question, it wouldnt make sense to break it up and would

Question

H7Q5

Sorry for the long question, it wouldnt make sense to break it up and would confuse everyone involved.

this is all the information im present with.

5. * Special Case for Least Squares (10 pts) Some special cases of least squares (a) Let's say we have a distribution of data which is best fit by a straight horizontal line through that passes through the origin. What are the values of your model parameters a, b? (b) What does this tell you about the components of b that are in the column space of X? Remember the equation Tb ???. What does this tell you about the direction of b with respect to the X column space? (c) Come up with your own data 12%, ye that will force least squares to produce a, b -[0, 0

Explanation / Answer

The line of best fit pasing through origin can be derived by using the simple linear model

Where y is the response variable is hypothesised as being a linear function of the explanatory variable x, and the two parameters a and b. The parameter a is called the intercept (the obtained value of y when x = 0), and b is the slope of the line (or the gradient, measured as the change in y in response to unit change in x).

Since the line is passing through origin hence a can only take one value and that is 0. Since when x=0 y=0 to, and there is no compulsion on value of b, the slope may either be negative or positive.

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