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) Line $B$clearly fits the collection of data points better than line $A$, according to the least squares criteria.

Step-by-step solution

Part (a) Step 1: Given information

The given data is

Part (a) Step 2: Explanation

Line A

$y=1.5+0.5x$

Line B

$y=1.125+0.375x$

Data points

The points and line A is drawn as

The points and line B is drawn as

Part (b) Step 1: Given information

The given points are

Part (b) Step 2: Explanation

Line A

$y=1.5+0.5x$

Line B

$y=1.125+0.375x$

Part (c) Step 1: Given information

The given points are

Part (c) Step 2: Explanation

The data points

Because the value of $\sum _{e^2}$is less in line $B$than in line $A$, it is evident that line $B$$y=1.125+0.375x$fits the set of data points better than line $A$$y=1.5+0.5x$according to the least square criteria.