Assignment 4 You are given two data sets (.xlsx files), stored the position of cancer cells during migration experiment in two different matrices, Collagen Matrix with a high concentration of collagen...

Using Rstudio answer the questions


Assignment 4 You are given two data sets (.xlsx files), stored the position of cancer cells during migration experiment in two  different matrices, Collagen Matrix with a high concentration of collagen and Collagen Matrix with a low concentration of collagen. The structure of data in each file is as follows:  • The first three columns store the cell coordinate point (X,Y,Z), X coordinate stored in first, Y in the second and Z the third column  • Column four contain the information about the time step.  • Column five is the ID of cells. Each cell has a unique ID.  Using the provided data sets, answer the following questions:  a) How many cancer cells were analyzed in each matrix? Write a program to answer this question. b) How many cells have a full track of migration? Write a program to answer this question. c) Find the speed for each individual cell in each matrix using the following formula:  Speed= (Net Cell Displacement)/total time   ** You may calculate the distance between two points in the space using:  ���������������� = √(���� − ����)�� + (���� − ����)�� + (���� − ����)��  where (��1, ��1, ��1) is the coordinate of the first point and (��2, ��2, ��2) is the   coordinate of the second point. The interval between two consecutive   time steps is 40 mins or (2/3)hour.  d) For cells migrated in the two matrices:  I. Create a boxplot of the migration speed.  II. Find the mean, median, standard deviation of the migration speed in each matrix  III. To the boxplots of part (I.) add  (-) The relevant data points to each boxplot (-) Add Mean Line segment   e) Does really the concertation of collagen (low and high) have impact on cell migration speed? Support your answer by applying a proper hypothesis testing method. Clearly define the  null and alternative hypothesis, explain response and predictor parameters used in your  analysis. 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