Question

a) Plot the data points and the first linear equation on one graph and the data points and the second linear equation on another.

(b) Construct tables for$x,y,e,e^2,\hat{y}$

(c) Determine which line fits the data points better according to the least-square criterion.

Short answer

(a)

(b)

(c) According to the least square criterion, it is clear that line A fits the set of data points better as compared to line B.

Step-by-step solution

Part (a) Step 1: Given information

The given points are

Part (a) Step 2: Explanation

Line A

$y=9-2x$

Line B

$y=6-x$

Data points

The data points and line A are drawn a

The data points and line B is drawn as

Part (b) Step 1: Given information

The given points are

Part (b) Step 2: Explanation

Data points

Line A

Line B

Part (c) Step 1: Given information

The given data is

Part (c) Step 2: Explanation

Data points

Because the value of $\sum e^2$is less in line $A$than in line $B$, it is evident that line $A$$y=9-2x$fits the collection of data points better than line $B$$y=6-x$, according to the least square criteria.