External link to Suppose the arithmetic function Y = f(N) satisfies Es(Y ) = 0 for all s = r > 1. Show that Y =…

# Suppose the arithmetic function Y = f(N) satisfies Es(Y ) = 0 for all s = r > 1. Show that Y =…

Suppose the arithmetic function Y = f(N) satisfies Es(Y ) = 0 for all s ≥ r > 1. Show that Y ≡ 0. (Hint: Prove that f(n) = 0 for all n by induction and sending s to ∞ in the equation ns Es(Y ) = 0.) Demonstrate that neither ϕ(n) nor μ(n) is completely multiplicative. Show that the Dirichlet convolution of two completely […]

External link to Let N1,…,Nm be an i.i.d. sample from the Zipf distribution with values n1,…,nm. If at least one.

# Let N1,…,Nm be an i.i.d. sample from the Zipf distribution with values n1,…,nm. If at least one.

Let N1,…,Nm be an i.i.d. sample from the Zipf distribution with values n1,…,nm. If at least one ni > 1, then prove that the maximum likelihood estimate of s is uniquely determined by the equation   What happens in the exceptional case when all ni = 1?

External link to Check that the Dirichlet inverse f[-1] of a multiplicative arithmetic function f is multiplicative..

# Check that the Dirichlet inverse f[-1] of a multiplicative arithmetic function f is multiplicative..

Check that the Dirichlet inverse f[−1] of a multiplicative arithmetic function f is multiplicative. (Hints: Assume otherwise, and consider the least product mn of two relatively prime natural numbers m and n with f[−1](mn) = f[−1](m)f[−1](n). Now apply the inductive definition of f[−1](mn).)

External link to Liouville’s arithmetic function is defined by

# Liouville’s arithmetic function is defined by

Read the notes and hints very carefully! (a) Develop a flowchart and then write a menu-driven C++ program to solve the following problem. Upon execution of the program, the menu will be displayed, properly centered as shown below. You will be using…

External link to For the juul data, fit a model for igf1 with interactions between age, sex, and Tanner stage for…

# For the juul data, fit a model for igf1 with interactions between age, sex, and Tanner stage for…

For the juul data, fit a model for igf1 with interactions between age, sex, and Tanner stage for those under 25 years old. Explain the interpretation of this model. Hint: A plot of the fitted values against age should be helpful. Use diagnostic plots to evaluate possible transformations of the dependent variable: untransformed, log, or square root.

External link to The parameters of the model can be estimated by the method of maximum likelihood. This is a quite…

# The parameters of the model can be estimated by the method of maximum likelihood. This is a quite…

The parameters of the model can be estimated by the method of maximum likelihood. This is a quite general technique, similar to the least-squares method in that it finds a set of parameters that optimizes a goodness-off it criterion (in fact, the least-squares method itself is a slightly modified maximum-likelihood procedure). The likelihood function L(β) is simply the probability of the entire observed data set […]

External link to Fit a logistic regression model to the graft.vs.host data set, predicting the gvhd response. Use…

# Fit a logistic regression model to the graft.vs.host data set, predicting the gvhd response. Use…

Fit a logistic regression model to the graft.vs.host data set, predicting the gvhd response. Use different transformations of the index variable. Reduce the model using backwards elimination. In the analyses of the malaria and graft.vs.host data, try using the confint function to find improved confidence intervals for the regression coefficients.

External link to In the malaria data set, analyze the risk of malaria with age and log-transformed antibody level as.

# In the malaria data set, analyze the risk of malaria with age and log-transformed antibody level as.

In the malaria data set, analyze the risk of malaria with age and log-transformed antibody level as explanatory variables. A probit regression is just like a logistic regression but uses a different link function. Try the analysis of the menarche variable in the juul data set with this link. Does the fit improve?

External link to In the bcmort data set, we defined the period and area factors in Exercise 10.2. Fit a Poisson…

# In the bcmort data set, we defined the period and area factors in Exercise 10.2. Fit a Poisson…

In the bcmort data set, we defined the period and area factors in Exercise 10.2. Fit a Poisson regression model to the data with age, period, and area as descriptors, as well as the three two-factor interaction terms. The interaction between period and area can be interpreted as the effect of screening.

External link to The philion data contain four small-sample EC50 experiments that are somewhat tricky to handle. We..

# The philion data contain four small-sample EC50 experiments that are somewhat tricky to handle. We..

The philion data contain four small-sample EC50 experiments that are somewhat tricky to handle. We suggest the model y = ymax/(1 + (x/β) α ). It may be useful to transform y by the square root since the data are counts, and this stabilizes the variance of the Poisson distribution. Consider how to obtain starting values for the model, and fit it with nls. The […]

External link to Try fitting the Gompertz model for girls in the Juul data. How would you go about testing whether…

# Try fitting the Gompertz model for girls in the Juul data. How would you go about testing whether…

Try fitting the Gompertz model for girls in the Juul data. How would you go about testing whether the same model fits both genders?(Theoretical) Continuing with the philion data, consider what happens if you modify the model to be y = ymax/(1 + x/β) α .

External link to Refer to Example 14.1. 1. How would you determine if Item.ID in bmv.rda includes leading or trailing

# Refer to Example 14.1. 1. How would you determine if Item.ID in bmv.rda includes leading or trailing

Refer to Example 14.1. 1. How would you determine if Item.ID in bmv.rda includes leading or trailing white spaces? 2. Follow the ideas introduced in the example to rid Item.ID from potential leading and trailing white spaces. In Example 14.8, we use the square transformation to relate tree diameter at breast height (DBH) to age. The transformation results in an apparent linear relationship. Why?

External link to What are the units of the intercept and slope of the following linearrelationships? 1. Y – height…

# What are the units of the intercept and slope of the following linearrelationships? 1. Y – height…

What are the units of the intercept and slope of the following linearrelationships? 1. Y – height (cm), x – weight (kg) 2. Y – basal metabolic rate (Kcal per hour), x – weight (kg) 3. Y – plants per m2, x – m2 Write an R script that produces Figure 14.4 and prints the summary of the linear model.

External link to Here are data about the number of classes missed and the corresponding score on the final exam for..

# Here are data about the number of classes missed and the corresponding score on the final exam for..

Here are data about the number of classes missed and the corresponding score on the final exam for 120 students in a statistics class (see exerciseskipping-class.txt): 1. Plot the scatter of the data. 2. Add to the plot points that show the mean score for those who missed one class, two classes, three and four. 3. Add to the plot the regression line. 4. On […]

External link to Import basal-metabolic-rate.txt’. The column names identify the order, family, species, mass (M, in.

# Import basal-metabolic-rate.txt’. The column names identify the order, family, species, mass (M, in.

Import basal-metabolic-rate.txt’. The column names identify the order, family, species, mass (M, in g), body temperature (T, in ◦C), and the basal metabolic rate (BMR, in kcal/hr). Next: 1. Plot the scatter of the numerical data in pairs and identify a pair of columns that indicate potential linear relationship. 2. Plot a scatter of the log of this pair. 3. Add the regression line to […]

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