Q. 4.43 - Elementary Statistics

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.

Step-by-Step Solution

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.

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.