Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
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If the data consist of two distinct points, then the least-squares line is just the line that passes through the two points.

What will be an ideal response?


It is true.

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Suppose that we are given two data points

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If we try to fit a straight line to these data points, the line will miss the first and the second data points by the amounts d1, d2, respectively.

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The principle of least squares states that the straight line L that fits the data points best is the one chosen by requiring that the sum of the squares

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be made as small as possible. In this case the smallest sum is zero.

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 when  and .

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Therefore, the required least-squares line is just the line that passes through the two points.


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A.

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C.

D.

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