An experiment to measure the macroscopic magnetic relaxation

An experiment to measure the macroscopic magnetic relaxation time in crystals (msec) as a function of the strength of the external biasing magnetic field (KG) yields the following data:

x          11.0     12.5     15.2     17.2     19.0     20.8     22.0     24.2     25.3     27.0     29.0

y          187      225      305      318      367      365      400      435      450      506      558

The summary statistics are Summation xi =223.2. Summation yi =4116, Summation xi2= 4877.5, Summation x iy i=90,096.1,

Summation yi2 =1,666782.   Assuming that the simple linear regression model is valid, compute the following:

a The least-square estimates of the slope and y-intercept.

b. The coefficient of determination, and interpret the results.

c. Compute the correlation coefficient for this data

d. What is the expected value of the relaxation time when the strength of the magnetic field is 17 KG.

e. Consider making two independent observations on the relaxation time, the first for strength of the magnetic field x1 = 15 KG and the second for x2 = 22 KG. What is the probability that the second observation will exceed the first with more than 130 msec.

Solution

A.

Using technology, we have

slope = 18.87349841
intercept = -8.778622211

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B.

Again, using technology, we have

r^2 = 0.980369393

which means that roughly 98.04% of the variation in magnetic relaxation time is explained by the external biasing magnetic field.

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C.

The correlation coefficint is simply the square root of the coefficient of determination,

r = 0.990136048

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