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Chapter 4: Q. 4.43 (page 173)

(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,e2,y^

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

Short Answer

Expert verified

(a)

(b)

(c) According to the least square criterion, the value of 鈭�e2is smaller in line B as compared to line A.

Step by step solution

01

Part (a) Step 1: Given information

The given data is

02

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

03

Part (b) Step 1: Given information

The given data is

04

Part (b) Step 2: Explanation

Line A

y=-1+3x

Line B

y=1+2x

05

Part (c) Step 1: Given information

The given data is

06

Part (c) Step 2: Explanation

The given data points are

Because the value of 鈭�e2is less in line Bthan in line A, it is evident that line A y=1+2xfits the collection of data points better than line By=-1+3x, according to the least square criteria.

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