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Regression Analysis - Heat Transfer

Please see the attached file for full problem description.

1. The following data are taken from a certain heat transfer test. The expected correlation equation is y=ax^ (b). Plot the data in an appropriate manner and use the method of least squares to obtain the best correlation.
y=aX^b then it says calculate a0 and a. It should be a and b.

X 2040 2580 2980 3220 3870 1690 2130 2420 2900 3310 1020 1240 1360 1710 2070
Y 33.2 32.0 42.7 57.8 126.0 17.4 21.4 27.8 52.1 43.1 18.8 19.2 15.1 12.9 78.5

(a) find a0, a and da0( or square root of "a0"), da (or square root of "a")
(b) Calculate the mean deviation of these data from the best correlation

2) For the following data points y is expected to be a power law function of x. obtain this quadratic function by means of a graphical plot and also by the method of least squares: function: y=a0 X ^(a1)
X 1 2 3 4 5
y 1.9 9.3 21.5 42.0 115.7

a) find a0, a, square root of "a" that gives the best fit for the data.
b) Plot the data


Solution Preview

Please see the attached files.

Part a
The best way to approach these problem is to first linearise the correlation equation:
Take ln of both sides
lny= lna + blnx
Hence we have a linear regression equation model for this problem. All we do now is plot the lny vs. lnx in Excel, and find the respective coefficients. I have plotted this in Excel file attached.
Once you plotted the series, select the Chart, go to Chart Options, Add trendline, select Linear and then ...

Solution Summary

The solution provides detailed explanations on the concept of regression analysis and step-by-step instructions in Word and Excel files.