How is the distance from the sun for planets in our solar system related to the mean temperature of each planet? To find out, a scatterplot that relates the natural log of the distance of each planet (including Pluto) from the sun in millions of miles and the natural log of the mean planetary temperature in Kelvin was created. A graph titled l n (Temperature) versus l n (distance) has l n (distance) on the x-axis, and l n (temperature) on the y-axis. Points are in a line with negative slope. A 5-column table with 2 rows. Column 1 is labeled Predictor with entries constant, l n distance. Column 2 is labeled coefficient with entries 7.9009, negative 0.4536. Column 3 is labeled S E Coefficient with entries 0.4381, 0.0706. Column 4 is labeled T with entries 18.03, negative 6.42. Column 5 is labeled P with entries 0.000, 0.004. S = 0.3446, r square = 85.5 percent, r square adjusted = 83.2 percent. Based on the scatterplot and computer output, a reasonable estimate of mean temperature in Kelvin for Saturn, which is 886.7 million miles away from the sun is: 4.822 degrees Kelvin because ŷ = −0.4536(In 886.7) + 7.9009 = 4.822. 124.2 degrees Kelvin because and e4.822 = 124.2. 709.0 degrees Kelvin because and e6.564 = 709.0. 0.05 degrees Kelvin because and e−3.008 = 0.049

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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How is the distance from the sun for planets in our solar system related to the mean temperature of each planet? To find out, a scatterplot that relates the natural log of the distance of each planet (including Pluto) from the sun in millions of miles and the natural log of the mean planetary temperature in Kelvin was created. A graph titled l n (Temperature) versus l n (distance) has l n (distance) on the x-axis, and l n (temperature) on the y-axis. Points are in a line with negative slope. A 5-column table with 2 rows. Column 1 is labeled Predictor with entries constant, l n distance. Column 2 is labeled coefficient with entries 7.9009, negative 0.4536. Column 3 is labeled S E Coefficient with entries 0.4381, 0.0706. Column 4 is labeled T with entries 18.03, negative 6.42. Column 5 is labeled P with entries 0.000, 0.004. S = 0.3446, r square = 85.5 percent, r square adjusted = 83.2 percent. Based on the scatterplot and computer output, a reasonable estimate of mean temperature in Kelvin for Saturn, which is 886.7 million miles away from the sun is: 4.822 degrees Kelvin because ŷ = −0.4536(In 886.7) + 7.9009 = 4.822. 124.2 degrees Kelvin because and e4.822 = 124.2. 709.0 degrees Kelvin because and e6.564 = 709.0. 0.05 degrees Kelvin because and e−3.008 = 0.0494.

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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