**Multiple linear regression model:**Try to establish a multiple linear regression model for the murder rate of the 50 states against the four variables: population, illiteracy, income, and frost. When you establish the model, please provide the theoretical details to determine the parameters of the model. When you get the model, try to use different statistical methods to validate it (I suggest to use R). The data can be downloaded here. (Only for one group)**Classification model:**A chemical analysis has been done for the wines grown in the same region in Italy but derived from three different cultivars. Try to design a classifier to classify the three kinds of wines based on the quantities of 13 constituents. When you design the classifier, please give the reasons why you choose this method, and also provide the theoretical details of the method. The data can be found here. (For two groups by using different methods)**Social network model:**For the follower network collected from GitHub, try to get a number of structural properties of the network, including the number of nodes, the average degree, the average clustering coefficient, the average network distance, and so on, and plot the degree distribution. Try to sample a subnetwork and visualize it by Cytoscape or Gephi. Try to establish network models for this social network according to the series of properties. The network data can be downloaded here. (For two groups to establish different network models)**Collective behavior model:**Try to establish mathematical models to explain the flocking of birds and the flashing in unison of fireflies. Make the reasonable assumptions when you establish the models, and provide gif pictures to show the dynamic results. (For two groups to establish different models)**Swarm intelligence model:**Design swarm intelligence algorithms, such as genetic algorithm and ant colony algorithm, to solve two of the optimization problems listed here. When you design the algorithm, please provide the theoretical details and the programming steps. When you get the results, give some suggestions to further improve the algorithm. (For two groups to adopt different algorithms)**Epidemic spreading on networks:**Use two kinds of networks, i.e., two-dimensional grid network and scale-free network. 1) For the first group, treat each node in a network as a city, people travel between linked cities (linked by some traffic means), and a person may be infected by another in the same city. Then try to use SIS model to explain the epidemic spreading on the traffic network. 2) For the second group, treat each node in a network as a person, a person can be infected by his/her neighbors, then use SIS model to explain the epidemic spreading on the social network. (For two groups to establish different models)**Fractal geometrical model:**Establish two different fractal geometrical models, one has the dimension in (1,2), and the other has the dimension in (2,3). Analyze the models and deduce the dimensions of the models. Visualize the fractal graphs generated by your models, use the box-covering method to estimate the dimensions of the graphs. (For two groups to establish different models)