At temperatures approaching absolute zero (-273°C), helium exhibits traits thatseem to defy many laws of Newtonian physics. An experiment has been conducted with heliumin solid form at various temperatures near absolute zero. The solid helium is placed in a dilutionrefrigerator along with a solid impure substance, and the fraction (in weight) of the impuritypassing through the solid helium is recorded. (This phenomenon of solid passing directingthrough solids is known as quantum tunneling.) Researchers wants to know the relationshipbetween temperature and proportion of impurity. They use a linear model with proportion ofimpurity being the response. The data is in the following:Temperature, x°C-262.0-265.0-256.0-267.0-270.0-272.0-272.4-272.7-272.8-272.9Proportion of impurity, y.315.202.204.620.715.935.957.906.985.987 a. Please write down the theoretical model and estimated linear model for this data.b. Test the null hypothesis that the true slope is 0; be sure to include null, alternative hypotheses,test method, and interpret your results.c. Use a 95% confidence interval to estimate the slope ß₁. Does the interval support thehypothesis that temperature is useful to predict the proportion of impurity passing throughhelium at alpha=0.05?d. Report and interpret the coefficient of determination for this modele. Find a 95% prediction interval for the percentage of impurity passing through solid helium at-272°C.

Given data as Temperature, x0C Proportion of impurity, y -262.0 0.315 -265.0 0.202 -256.0…

Answered: a. Please write down the theoretical…

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 engineer at a company wants to model the relationship between the yield (y) and three variables: pressure (x1), volume (x2) and temperature (x3). Data is collected and the output of the statistical analysis is displayed table below. i. From appropriate statistical tests, determine the relationship between yield and the three variables, Use a 5% significance level where required.
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please help.
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