Set by Dr. Daniel Perley

Please attach your answers with R command lines used.

The file oscillate.csv contains measurements of an oscillating source.The response variable D (displacement) is thought to be a sinusoidal function of the measurement phase, w.Mathematically, the underlying behavior is expected to be governed by one of the following four equations:

Model 0: $D = k$

Model 1: $D = k + A_1\,{ m sin}(w) + B_1\,{ m cos}(w)$

Model 2: $D = k + A_1\,{ m sin}(w) + B_1\,{ m cos}(w) + A_2\,{ m sin}(2w) + B_2\,{ m cos}(2w)$

Model 3: $D = k + A_1\,{ m sin}(w) + B_1\,{ m cos}(w) + A_2\,{ m sin}(2w) + B_2\,{ m cos}(2w) + A_3\,{ m sin}(3w) + B_3\,{ m cos}(3w)$

a. Is this a linear model or a nonlinear model, in regards to the connection between the response variable and the model parameters?

b. Is this series of models nested or non-nested?

c. Which of these four models, if any, can you rule out?Provide a $p$-value associated with the most complex model that you can rule out.

d. Provide estimates of the parameter values, and the standard errors on those values, for all terms in the preferred model (i.e., the simplest model that is not ruled out).

oscillate.csv data set a link

https://1drv.ms/u/s!AgOhBzX2T2W6uyGIKyZTh9Gds5J5?e=7RIW2R