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, the value of $\sum _{e^2}$is smaller in line B as compared to line A.

Step-by-step solution

Part (a) Step 1: Given information

The given data is

Part (a) Step 2: Explanation

Line A

$y=-1+3x$

Line B

$y=1+2x$

Data points

The data points and line A are drawn as

The data points and line B are drawn as

Part (b) Step 1: Given information

The given data is

Part (b) Step 2: Explanation

Line A

$y=-1+3x$

Line B

$y=1+2x$

Part (c) Step 1: Given information

The given data is

Part (c) Step 2: Explanation

The given data points are

Because the value of $\sum _{e^2}$is less in line $B$than in line $A$, it is evident that line $A$ $y=1+2x$fits the collection of data points better than line $B$$y=-1+3x$, according to the least square criteria.