The question considered in this exercise concerns whether the solution obtained using regression reduces to the solution obtained using interpolation in the case of when the number of data points...

The question considered in this exercise concerns whether the solution obtained using regression reduces to the solution obtained using interpolation in the case of when the number of data points equals the number of parameters.

(a) The least squares solution in (8.12) is for the model function
() =

₁
+

₂
. Show that the solution reduces to the point-slope formula in the case of when
 = 2 and

<sub>1

2</sub>. In other words, the regression solution produces the interpolation solution.

(b) In the case of when
 = 2,

<sub>1

2</sub>, and
() =

₁
+

₂
, show that the values of

₁
and

₂
obtained using the point-slope formula produce the minimum error for

₁,


_∞
, and


_D

(these are defined in Section 8.3.3).