# Sequence / Linear functions

Anonymous

Question description

1. Consider the sequence s defined by:

S_n=n^2-3n+3,  for n≥1

a) Find

∑_(i=1)^4▒s_i =∑_(i=1)^4▒(i^2-3n+3) =

b) Find

∑_(k=3)^5▒s_k =

Consider the following points:

(x_1,y_1 )=(2,2),
(x_2,y_2 )=(2,4),
(x_3,y_3 )=(3,4),
(x_4,y_4 )=(4,3),
(x_5,y_5 )=(4,4),
(x_6,y_6 )=(4,5),
(x_7,y_7 )=(6,4),
(x_8,y_8 )=(6,5).

Also consider the following linear functions:

f_1 (x)=1/2 x+1
f_2 (x)=1/2 x+2
f_3 (x)=4

Evaluate which of the three linear functions is a better linear regression function for the given point.  Let f be any of the functions.  Then for each function you will have to compute the value:

SE=∑_(i=1)^8▒(y_i-f(x_i))^2

Then you will choose the best regression function (of the three) as the one with the smallest value for SE.

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