Studies have shown that people who suffer sudden cardiac arrest have a better chance of survival if a defibrillator shock is administered very soon after cardiac arrest. How is survival rate related to the time between when cardiac arrest occurs and when the defibrillator shock is delivered? The accompanying data give y = survival rate (percent) and x = mean call-to-shock time (minutes) for a cardiac rehabilitation center (in which cardiac arrests occurred while victims were hospitalized and so the call-to-shock time tended to be short) and for four communities of different sizes. Mean call-to-shock time, x 2 6 7 9 12 Survival rate, y 91 46 31 6 3 (a) Construct a scatterplot for these data. A scatterplot has 5 points. The horizontal axis is labeled "x" and has values from 0 to 100. The vertical axis is labeled "y" and has values from 0 to 13. 1 point is plotted at approximately (2.5, 2). 4 points are plotted in an almost straight line from approximately (5, 6) up and right to approximately (90, 12). A scatterplot has 5 points. The horizontal axis is labeled "x" and has values from 0 to 13. The vertical axis is labeled "y" and has values from 0 to 100. 1 point is plotted at approximately (2, 2.5). 4 points are plotted in an almost straight line from approximately (6, 5) up and right to approximately (12, 90). A scatterplot has 5 points. The horizontal axis is labeled "x" and has values from 0 to 100. The vertical axis is labeled "y" and has values from 0 to 13. 1 point is plotted at approximately (2.5, 12). 4 points are plotted in an almost straight line from approximately (5, 9) down and right to approximately (90, 2). A scatterplot has 5 points. The horizontal axis is labeled "x" and has values from 0 to 13. The vertical axis is labeled "y" and has values from 0 to 100. 1 point is plotted at approximately (12, 2.5). 4 points are plotted in an almost straight line from approximately (2, 90) down and right to approximately (9, 5). How would you describe the relationship between mean call-to-shock time and survival rate? There is a strong positive relationship. The relationship is close to being linear, particularly if the point with the lowest x value is disregarded. If that point is included then there is the suggestion of a curve.There is a strong negative relationship. The relationship is close to being linear, particularly if the point with the highest x value is disregarded. If that point is included then there is the suggestion of a curve. There is a strong positive relationship. The relationship is close to being linear, particularly if the point with the highest x value is disregarded. If that point is included then there is the suggestion of a curve.There is a strong negative relationship. The relationship is close to being linear, particularly if the point with the lowest x value is disregarded. If that point is included then there is the suggestion of a curve. (b) Find the equation of the least-squares line. (Round your values to four decimal places.) ŷ = + x (c) Use the least-squares line to predict survival rate for a community with a mean call-to-shock time of 8 minutes. (Round your answer to three decimal places.)

Studies have shown that people who suffer sudden cardiac arrest have a better chance of survival if a defibrillator shock is administered very soon after cardiac arrest. How is survival rate related to the time between when cardiac arrest occurs and when the defibrillator shock is delivered? The accompanying data give y = survival rate (percent) and x = mean call-to-shock time (minutes) for a cardiac rehabilitation center (in which cardiac arrests occurred while victims were hospitalized and so the call-to-shock time tended to be short) and for four communities of different sizes. Mean call-to-shock time, x 2 6 7 9 12 Survival rate, y 91 46 31 6 3 (a) Construct a scatterplot for these data. A scatterplot has 5 points. The horizontal axis is labeled "x" and has values from 0 to 100. The vertical axis is labeled "y" and has values from 0 to 13. 1 point is plotted at approximately (2.5, 2). 4 points are plotted in an almost straight line from approximately (5, 6) up and right to approximately (90, 12). A scatterplot has 5 points. The horizontal axis is labeled "x" and has values from 0 to 13. The vertical axis is labeled "y" and has values from 0 to 100. 1 point is plotted at approximately (2, 2.5). 4 points are plotted in an almost straight line from approximately (6, 5) up and right to approximately (12, 90). A scatterplot has 5 points. The horizontal axis is labeled "x" and has values from 0 to 100. The vertical axis is labeled "y" and has values from 0 to 13. 1 point is plotted at approximately (2.5, 12). 4 points are plotted in an almost straight line from approximately (5, 9) down and right to approximately (90, 2). A scatterplot has 5 points. The horizontal axis is labeled "x" and has values from 0 to 13. The vertical axis is labeled "y" and has values from 0 to 100. 1 point is plotted at approximately (12, 2.5). 4 points are plotted in an almost straight line from approximately (2, 90) down and right to approximately (9, 5). How would you describe the relationship between mean call-to-shock time and survival rate? There is a strong positive relationship. The relationship is close to being linear, particularly if the point with the lowest x value is disregarded. If that point is included then there is the suggestion of a curve.There is a strong negative relationship. The relationship is close to being linear, particularly if the point with the highest x value is disregarded. If that point is included then there is the suggestion of a curve. There is a strong positive relationship. The relationship is close to being linear, particularly if the point with the highest x value is disregarded. If that point is included then there is the suggestion of a curve.There is a strong negative relationship. The relationship is close to being linear, particularly if the point with the lowest x value is disregarded. If that point is included then there is the suggestion of a curve. (b) Find the equation of the least-squares line. (Round your values to four decimal places.) ŷ = + x (c) Use the least-squares line to predict survival rate for a community with a mean call-to-shock time of 8 minutes. (Round your answer to three decimal places.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Question

The accompanying data give y = survival rate (percent) and x = mean call-to-shock time (minutes) for a cardiac rehabilitation center (in which cardiac arrests occurred while victims were hospitalized and so the call-to-shock time tended to be short) and for four communities of different sizes.

Mean call-to-shock time, x	2	6	7	9	12
Survival rate, y	91	46	31	6	3

(a)

Construct a scatterplot for these data.

A scatterplot has 5 points.

The horizontal axis is labeled "x" and has values from 0 to 100.
The vertical axis is labeled "y" and has values from 0 to 13.
1 point is plotted at approximately (2.5, 2).
4 points are plotted in an almost straight line from approximately (5, 6) up and right to approximately (90, 12).

A scatterplot has 5 points.

The horizontal axis is labeled "x" and has values from 0 to 13.
The vertical axis is labeled "y" and has values from 0 to 100.
1 point is plotted at approximately (2, 2.5).
4 points are plotted in an almost straight line from approximately (6, 5) up and right to approximately (12, 90).

A scatterplot has 5 points.

The horizontal axis is labeled "x" and has values from 0 to 100.
The vertical axis is labeled "y" and has values from 0 to 13.
1 point is plotted at approximately (2.5, 12).
4 points are plotted in an almost straight line from approximately (5, 9) down and right to approximately (90, 2).

A scatterplot has 5 points.

The horizontal axis is labeled "x" and has values from 0 to 13.
The vertical axis is labeled "y" and has values from 0 to 100.
1 point is plotted at approximately (12, 2.5).
4 points are plotted in an almost straight line from approximately (2, 90) down and right to approximately (9, 5).

How would you describe the relationship between mean call-to-shock time and survival rate?

There is a strong positive relationship. The relationship is close to being linear, particularly if the point with the lowest x value is disregarded. If that point is included then there is the suggestion of a curve.There is a strong negative relationship. The relationship is close to being linear, particularly if the point with the highest x value is disregarded. If that point is included then there is the suggestion of a curve. There is a strong positive relationship. The relationship is close to being linear, particularly if the point with the highest x value is disregarded. If that point is included then there is the suggestion of a curve.There is a strong negative relationship. The relationship is close to being linear, particularly if the point with the lowest x value is disregarded. If that point is included then there is the suggestion of a curve.

(b)

Find the equation of the least-squares line. (Round your values to four decimal places.)

ŷ = +

(c)

Use the least-squares line to predict survival rate for a community with a mean call-to-shock time of 8 minutes. (Round your answer to three decimal places.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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