Answered: A funding agency has performed an…

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 funding agency has performed an internal study in which the number of loan requests (Y variable, in thousands) is related with the interest rate in percentage terms (X variable) applied to these loans. The following information is known: the mean of x= 5, the mean of y = 20000, the standard deviation of x = 1.5, the standard deviation of y = 5000 and the covariance of x and y = -5400.

First, obtain the regression line that allows to estimate the number of loan requests (Y) as a function of its interest rate in percentage terms (X). Interpret the value of the obtained coefficients.

Then, obtain an appropriate indicator of the goodness of fit of this model and discuss the result. Regarding the variability, obtain the explained and the error components of the variance. Interpret all the results

Finally, Estimate the number of loans requests we can expect with an interest rate of 3.5%. Analyze the reliability of this prediction. What is the needed assumption to perform this prediction?

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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