Electric resistance in copper wire changes with the temperature of the wire. If C(t) is the electric resistance at temperature t, in degrees Fahrenheit, then the resistance ratio C(t)/C(0) can bemeasured.Temperature tin degreesC(t) ratioC(0)0.1101.0393201.0798301.1215401.1644(a) Use regression to find a quadratic formula for the ratio C(t)/C(0) as a function of temperature t. Do not round the regression parameters.C(t)C(0)0.9988+ 0.00411T%3D(b) At what temperature is the electric resistance double that at 0 degrees? (Round your answer to two decimal places.)t =(c) Suppose that you have designed a household appliance to be used at room temperature (76 degrees) and you need to have the wire resistance inside the appliance accurate to plus orminus 10% of the predicted resistance at 76 degrees.(i) What resistance ratio do you predict at 76 degrees? (Use four decimal places.)

(a) The quadratic regression equation is written as : Y=a+bx+cx2 First create another column for t2 and then run regression taking the ratio as dependent variable and t, t2 as independent variable. Let the ratio C(t)/C(0) be denoted as Y and the independent variables be t, t2. t C(t)/C(0)=Y t2 0 1 0 10 1.0393 100 20 1.0798 400 30 1.1215 900 40 1.1644 1600 Running the regression in SPSS, following results are obtained :The quadratic regression equation is : Y=1+0.004t+0.000006t2 (b) At zero degrees the electric resistance is 1 2×1=1+0.004t+0.000006t22-1=0.004t+0.000006t20.000006t2+0.004t-1=0 Solve for the roots of the quadratic equation. The roots obtained are : 193.73 , -860.380(approximately) (c) Substitute the temperature in the quadratic equation obtained to calculate the predicted resistance.

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Electric resistance in copper wire changes with the temperature of the wire. If C(t) is the electric resistance at temperature t, in degrees Fahrenheit, then the resistance ratio C(t)/C(0) can be measured. Temperature t in degrees C(t ratio C(0) 1. 10 1.0393 20 1.0798 1.1215 30 40 1.1644 (a) Use regression to find a quadratic formula for the ratio C(t)/C(0) as a function of temperature t. Do not round the regression parameters. CO - 0.9988+0.004117 C(0) (b) At what temperature is the electric resistance double that at 0 degrees? (Round your answer to two decimal places.) (c) Suppose that you have designed a household appliance to be used at room temperature (76 degrees) and you need to have the wire resistance inside the appliance accurate to plus or minus 10% of the predicted resistance at 76 degrees. (1) What resistance ratio do you predict at 76 degrees? (Use four decimal places.)

Electric resistance in copper wire changes with the temperature of the wire. If C(t) is the electric resistance at temperature t, in degrees Fahrenheit, then the resistance ratio C(t)/C(0) can be measured. Temperature t in degrees C(t ratio C(0) 1. 10 1.0393 20 1.0798 1.1215 30 40 1.1644 (a) Use regression to find a quadratic formula for the ratio C(t)/C(0) as a function of temperature t. Do not round the regression parameters. CO - 0.9988+0.004117 C(0) (b) At what temperature is the electric resistance double that at 0 degrees? (Round your answer to two decimal places.) (c) Suppose that you have designed a household appliance to be used at room temperature (76 degrees) and you need to have the wire resistance inside the appliance accurate to plus or minus 10% of the predicted resistance at 76 degrees. (1) What resistance ratio do you predict at 76 degrees? (Use four decimal places.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

Electric resistance in copper wire changes with the temperature of the wire. If C(t) is the electric resistance at temperature t, in degrees Fahrenheit, then the resistance ratio C(t)/C(0) can be
measured.
Temperature t
in degrees
C(t) ratio
C(0)
0.
1
10
1.0393
20
1.0798
30
1.1215
40
1.1644
(a) Use regression to find a quadratic formula for the ratio C(t)/C(0) as a function of temperature t. Do not round the regression parameters.
C(t)
C(0)
0.9988+ 0.00411T
%3D
(b) At what temperature is the electric resistance double that at 0 degrees? (Round your answer to two decimal places.)
t =
(c) Suppose that you have designed a household appliance to be used at room temperature (76 degrees) and you need to have the wire resistance inside the appliance accurate to plus or
minus 10% of the predicted resistance at 76 degrees.
(i) What resistance ratio do you predict at 76 degrees? (Use four decimal places.)

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