A statistical program is recommended. Consider the following data for two variables, x and y. xi 4 5 7 8 10 12 12 22 yi 12 14 16 15 17 20 24 19 (a) Compute the standardized residuals for these data. (Round your answers to two decimal places.) xi yi Standardized Residuals 4 12 5 14 7 16 8 15 10 17 12 20 12 24 22 19 Do the data include any outliers? Explain. There are no standardized residuals that are less than −2 or greater than +2, so there are no possible outliers.There is one standardized residuals that is less than −2 or greater than +2, so there is one possible outlier. There are two standardized residuals that are less than −2 or greater than +2, so there are two possible outliers.There are more than two standardized residuals that are less than −2 or greater than +2, so there are more than two possible outliers. (b) Compute the leverage values for these data. (Round your answers to two decimal places.) xi yi Leverage Values 4 12 5 14 7 16 8 15 10 17 12 20 12 24 22 19 Do there appear to be any influential observations in these data? Explain. Minitab identifies an observation as having high leverage if hi > 6 n; for these data, 6 n = . Since the leverage for the observation at (xi, yi) = is greater than 6 n, we conclude that this observation is an influential observation. (c) Develop a scatter diagram for these data. A scatter diagram has 8 points plotted on it. The horizontal axis ranges from 0 to 25 and is labeled: x. The vertical axis ranges from 0 to 30

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

A statistical program is recommended.

Consider the following data for two variables, x and y.

x_i	4	5	7	8	10	12	12	22
y_i	12	14	16	15	17	20	24	19

(a)

Compute the standardized residuals for these data. (Round your answers to two decimal places.)

x_i	y_i	Standardized Residuals
4	12
5	14
7	16
8	15
10	17
12	20
12	24
22	19

Do the data include any outliers? Explain.

There are no standardized residuals that are less than −2 or greater than +2, so there are no possible outliers.There is one standardized residuals that is less than −2 or greater than +2, so there is one possible outlier. There are two standardized residuals that are less than −2 or greater than +2, so there are two possible outliers.There are more than two standardized residuals that are less than −2 or greater than +2, so there are more than two possible outliers.

(b)

Compute the leverage values for these data. (Round your answers to two decimal places.)

x_i	y_i	Leverage Values
4	12
5	14
7	16
8	15
10	17
12	20
12	24
22	19

Do there appear to be any influential observations in these data? Explain.

Minitab identifies an observation as having high leverage if

h_i >

;

for these data,

= .

Since the leverage for the observation at

(x_i, y_i) =

is greater than

we conclude that this observation is an influential observation.

(c)

Develop a scatter diagram for these data.

A scatter diagram has 8 points plotted on it. The horizontal axis ranges from 0 to 25 and is labeled: x. The vertical axis ranges from 0 to 30 and is labeled: y. The points are plotted from left to right in a downward, diagonal direction starting from the upper left corner of the diagram. The points are between 4 to 22 on the horizontal axis and between 12 to 24 on the vertical axis. Most of the points are plotted fairly close together, although there is a large gap between the 2 points at x = 12 and the point at x = 22. The maximum y-value is located at x = 5.

A scatter diagram has 8 points plotted on it. The horizontal axis ranges from 0 to 25 and is labeled: x. The vertical axis ranges from 0 to 30 and is labeled: y.The points are plotted from left to right in a downward, diagonal direction starting from the upper left corner of the diagram. The points are between 4 to 22 on the horizontal axis and between 12 to 24 on the vertical axis. Most of the points are plotted fairly close together, although there is a large gap between the 2 points at x = 12 and the point at x = 22. The maximum y-value is located at x = 4.

A scatter diagram has 8 points plotted on it. The horizontal axis ranges from 0 to 25 and is labeled: x. The vertical axis ranges from 0 to 30 and is labeled: y. The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram. The points are between 4 to 22 on the horizontal axis and between 12 to 24 on the vertical axis. Most of the points are plotted fairly close together, although there is a large gap between the 2 points at x = 12 and the point at x = 22. The maximum y-value is located at x = 22.

A scatter diagram has 8 points plotted on it. The horizontal axis ranges from 0 to 25 and is labeled: x. The vertical axis ranges from 0 to 30 and is labeled: y. The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram. The points are between 4 to 22 on the horizontal axis and between 12 to 24 on the vertical axis. Most of the points are plotted fairly close together, although there is a large gap between the 2 points at x = 12 and the point at x = 22. The maximum y-value is located at x = 12.

Does the scatter diagram indicate any influential observations? Explain.

The scatter diagram indicates that there are no influential observations because no points have a large influence on the estimated regression line.The scatter diagram indicates that there is one influential observation because one point has a large influence on the estimated regression line. The scatter diagram indicates that there are two influential observations because two points have a large influence on the estimated regression line.The scatter diagram indicates that there are more than two influential observations because more than two points have a large influence on the estimated regression line.

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