Task of the day(a) If Z=aX+ bY and r is the correlation coefficient between X and Y,show that o²=a²oy² + b²oy² + 2abrox Oy.(b) Show that the correlation coefficient r between two random variables X and Y is givenbyr = (0x² +0²-0² x - y) / 20x Oy,where ox, oy and ox-y are the standard deviations of X, Y and X - Y respectively.

The variance of a random variable X, denoted by Var(X), is defined as a measure of dispersion of the…

Answered: Task of the day (a) If Z=aX+ bY and r…

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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An agricultural field trial compares the yield of two varieties of corn. The researchers divide in half each of 9 fields of land in different locations and plant each corn variety in one half of each plot. After harvest, the yields are compared in bushels per acre at each location. The 9 differences (Variety A - Variety B) give x¯=3.35x¯=3.35 and s=4.61s=4.61. Does this sample provide evidence that Variety A had a higher yield than Variety B? (a) State the null and alternative hypotheses: (Type "mu" for the symbol μμ , e.g. mu >> 1 for the mean is greater than 1, mu << 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1)H0H0 : HaHa : (b) Find the test statistic, t = (c) Answer the question: Does this sample provide evidence that Variety A had a higher yield than Variety B? (Use a 5% level of significance)(Type: Yes or No)
A scientist wants to develop a model to describe the relationship between the average daily temperature, x °C, and her household’s daily energy consumption, y kWh, in winter. A random sample of the average daily temperature and her household’s daily energy consumption are taken from 10 winter days and shown in the table. x -0.4 -0.2 0.3 0.8 1.1 1.4 1.8 2.1 2.5 2.6 y 28 30 26 25 26 27 26 24 22 21 You may use: Sy=255 Sxy=283.8 Syy= 64.5 Find a value for the product moment correlation coefficient r for this data Explain what the value of the product moment corelation tells you about the relationship between daily temperature and the household energy consumption.
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