Question

Construct a scatterplot for the data in the following table.

X	.5	1	1.5
y	2	1	3

a. Plot the following two lines on your scatterplot: y = 3 - x and y = 1 + x

b. Which of these lines would you choose to characterize the relationship between x and y? Explain.

c. Show that the sum of the prediction errors for both of these lines equals 0.

d. Which of these lines has the smaller SSE?

e. Determine the data's least-squares line and compare it to the two lines described in part a.

Short answer

Answer

1. Fig. 1 Scatterplot
2. Fig. 2 Table
3. Fig. 3 Table
4. Fig. 4 Table, Fig. 2 Table
5. Fig. 6 Table

Step-by-step solution

Introduction

The total variance of the response values from the match to the response values is calculated by this statistic. The sum square of regression is another name for it, and it's denoted as SSE.

(a) Draw a scatterplot

(b) The relationship between x and y

The lines I used to characterize the relation between x and y are:

$\mathbf{\text{Y = 1 + x}}$

The data is compared to a close-ratio of x and y.

(c) Show that the sum of the prediction errors for both of these lines equals 0

The sum of the prediction errors for both of these lines is:

Therefore, the sum of the prediction errors for both lines equals 0.

(d) Find which line has a smaller SSE

$\mathbf{\text{y = 3}}\mathbf{-}\mathbf{\text{x}}$

$\mathbf{\text{y = 1 + x}}$

We may derive SSE from the two tables above:

$\mathbf{\sum }\mathbf{\text{(y}}\mathbf{-}\overline{\mathbf{\text{y}}}{\mathbf{\text{)}}}^{\mathbf{\text{2}}}\mathbf{\text{=0.25}}$

Therefore, both the lines have the same SSE.

(e) Determine the data's least-squares line and compare it to the two lines described in part a

The least-square line is $\mathbf{\text{Y = 1 + x}}$.

From part the line equation, i.e., $\mathbf{\text{Y = 1 + x}}$equivalent to the given data.