## onstruct a model using the two explanatory variables that you found in part (b). How well does this model predict TotalSleep?

Biologists are interested in determining factors that predict the amount of time an animal sleeps during the day. To investigate the possibilities, Allison and Ciccetti (1976) gathered information about 62 different mammals. Their data is presented in the sample data table Sleeping Animals.jmp. The variables describe body weight, brain weight, total time spent sleeping in two different states (Dreaming and NonDreaming), life span, and gestation time. The researchers also calculated indices to represent predation (1 meaning unlikely to be preyed upon, 5 meaning likely to be preyed upon), exposure (1 meaning that the animal sleeps in a well-protected den, 5 meaning most exposure), and an overall danger index, based on predation, exposure, and other factors (1 meaning least danger from other animals, 5 meaning most danger).

(a) Use the Fit Y By X platform to examine the single-variable relationships between TotalSleep and the other variables. Which two variables look like they have the highest correlation with TotalSleep?

b) If you remove NonDreaming from consideration, which two variables appear to be most correlated with TotalSleep?

(c) Construct a model using the two explanatory variables that you found in part (b). How well does this model predict TotalSleep?

(d) Construct a model using P-Value Threshold as the Stopping Rule and forward stepwise regression (still omitting NonDreaming), with 0.10 as the probability to enter and leave the model. Compare this model to the one you constructed in part (c).

(e) Construct a new model using mixed stepwise regression, with 0.10 as the probability to enter and leave the model. Compare this model to the other models that you have found. Which is the most effective at predicting total amount of sleep?

(f) Comment on the generalizability of this model. Would it be safe to use it to predict sleep times for a llama? Or a gecko? Explain your reasoning.

(g) Explore models that predict sleep in the dreaming and non-dreaming stages. Do the same predictors appear to be valid?

### Write the integral expression for the two-parameter output correlation function  over the time intervals .

Consider the following mean-square differential equation, driven by a WSS random process  with psd The differential equation is subject to the initial condition , where the random variable  has zero-mean, variance 5, and….

### Repeat the corresponding segment of the correlation function periodically.

If a stationary random process is periodic, then we can represent it by a Fourier series with orthogonal coefficients. This is not true in general when the random process, though….

### Show that an m.s. derivative process  exists here.

Certain continuous time communications channel can be modeled as signal plus an independent additive noise (a) The receiver must process  for the purpose of determining the value of the message random….