Answered: Does a high value of r2 imply that two…

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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Does a high value of r² imply that two variables are causally related? Explain.
In your own words, explain the difference between an interval estimate of the mean value of y for a given x and an interval estimate for an individual value of y for a given x.
What is the purpose of testing whether ᵝ₁=0? If we reject ᵝ₁=0, does it imply a good fit?

The admissions officer for Clearwater College developed the following estimated regression equation relating the final college GPA to the student’s SAT mathematics score and high-school GPA.

yˆ= -1.41 + .0235x1 + .00486x2

Where

x1 = high-school grade point average

x2 = SAT mathematics score

y = final college grade point average

Interpret the coefficients in this estimated regression equation.

Estimate the final college GPA for a student who has a high-school average of 84 and a score of 540 on the SAT mathematics test.

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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