Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 7 6 10 13 (a) Develop a scatter diagram for these data. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 4 to 13 on the vertical axis. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. The points are plotted from left to right in increments of 1 in a downward, diagonal direction starting in the upper left corner of the diagram. The points are between 4 to 13 on the vertical axis. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. The points are plotted from left to right in increments of 1 starting in the upper left corner of the diagram. The first 2 points are between 10 to 13 on the vertical axis. The next 3 points are between 4 to 7 on the vertical axis. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 3 to 12 on the vertical axis. (b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? There appears to be a negative linear relationship between x and y.There appears to be a positive linear relationship between x and y. There appears to be no noticeable relationship between x and y. (c) Try to approximate the relationship between x and y by drawing a straight line through the data. A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. A straight line with negative slope is imposed onto the diagram to approximate the relationship between x and y implied by the points, with 3 points lying below the line. The points are plotted from left to right in increments of 1 starting in the upper left corner of the diagram. The first 2 points are between 10 to 13 on the vertical axis. The next 3 points are between 4 to 7 on the vertical axis. A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. A straight line with positive slope is imposed onto the diagram to approximate the relationship between x and y implied by the points, with 2 points lying below the line. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 3 to 12 on the vertical axis. A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. A straight line with negative slope is imposed onto the diagram to approximate the relationship between x and y implied by the points, with 2 points lying below the line. The points are plotted from left to right in increments of 1 in a downward, diagonal direction starting in the upper left corner of the diagram. The points are between 4 to 13 on the vertical axis. A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. A straight line with positive slope is imposed onto the diagram to approximate the relationship between x and y implied by the points, with 2 points lying below the line. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 4 to 13 on the vertical axis. (d) Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2 and b0 = y − b1x. ŷ = .5+2.5x (e) Use the estimated regression equation to predict the value of y when x = 2.

Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 7 6 10 13 (a) Develop a scatter diagram for these data. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 4 to 13 on the vertical axis. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. The points are plotted from left to right in increments of 1 in a downward, diagonal direction starting in the upper left corner of the diagram. The points are between 4 to 13 on the vertical axis. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. The points are plotted from left to right in increments of 1 starting in the upper left corner of the diagram. The first 2 points are between 10 to 13 on the vertical axis. The next 3 points are between 4 to 7 on the vertical axis. A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 3 to 12 on the vertical axis. (b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? There appears to be a negative linear relationship between x and y.There appears to be a positive linear relationship between x and y. There appears to be no noticeable relationship between x and y. (c) Try to approximate the relationship between x and y by drawing a straight line through the data. A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. A straight line with negative slope is imposed onto the diagram to approximate the relationship between x and y implied by the points, with 3 points lying below the line. The points are plotted from left to right in increments of 1 starting in the upper left corner of the diagram. The first 2 points are between 10 to 13 on the vertical axis. The next 3 points are between 4 to 7 on the vertical axis. A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. A straight line with positive slope is imposed onto the diagram to approximate the relationship between x and y implied by the points, with 2 points lying below the line. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 3 to 12 on the vertical axis. A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. A straight line with negative slope is imposed onto the diagram to approximate the relationship between x and y implied by the points, with 2 points lying below the line. The points are plotted from left to right in increments of 1 in a downward, diagonal direction starting in the upper left corner of the diagram. The points are between 4 to 13 on the vertical axis. A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. A straight line with positive slope is imposed onto the diagram to approximate the relationship between x and y implied by the points, with 2 points lying below the line. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 4 to 13 on the vertical axis. (d) Develop the estimated regression equation by computing the values of b0 and b1 using b1 = Σ(xi − x)(yi − y) Σ(xi − x)2 and b0 = y − b1x. ŷ = .5+2.5x (e) Use the estimated regression equation to predict the value of y when x = 2.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Given are five observations for two variables, x and y.

x_i	1	2	3	4	5
y_i	4	7	6	10	13

(a)

Develop a scatter diagram for these data.

A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 4 to 13 on the vertical axis.

A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. The points are plotted from left to right in increments of 1 in a downward, diagonal direction starting in the upper left corner of the diagram. The points are between 4 to 13 on the vertical axis.

A scatter diagram has 5 points plotted on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. The points are plotted from left to right in increments of 1 starting in the upper left corner of the diagram. The first 2 points are between 10 to 13 on the vertical axis. The next 3 points are between 4 to 7 on the vertical axis.

(b)

What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

There appears to be a negative linear relationship between x and y.There appears to be a positive linear relationship between x and y. There appears to be no noticeable relationship between x and y.

(c)

Try to approximate the relationship between x and y by drawing a straight line through the data.

A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. A straight line with negative slope is imposed onto the diagram to approximate the relationship between x and y implied by the points, with 3 points lying below the line. The points are plotted from left to right in increments of 1 starting in the upper left corner of the diagram. The first 2 points are between 10 to 13 on the vertical axis. The next 3 points are between 4 to 7 on the vertical axis.

A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. A straight line with positive slope is imposed onto the diagram to approximate the relationship between x and y implied by the points, with 2 points lying below the line. The points are plotted from left to right in increments of 1 in an upward, diagonal direction starting in the lower left corner of the diagram. The points are between 3 to 12 on the vertical axis.

A scatter diagram has 5 points on it. The horizontal axis ranges from 0 to 6 and is labeled: x. The vertical axis ranges from 0 to 18 and is labeled: y. A straight line with negative slope is imposed onto the diagram to approximate the relationship between x and y implied by the points, with 2 points lying below the line. The points are plotted from left to right in increments of 1 in a downward, diagonal direction starting in the upper left corner of the diagram. The points are between 4 to 13 on the vertical axis.

(d)

Develop the estimated regression equation by computing the values of

b₀

and

b₁

using

b₁ =

Σ(x_i − x)(y_i − y)

Σ(x_i − x)²

and

b₀ = y − b₁x.

ŷ =

.5+2.5x

(e)

Use the estimated regression equation to predict the value of y when

x = 2.

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