A research facility is evaluating five different processes of extracting starch from corn flour.

The percent yield of starch is the response of interest. The data is shown below:

Process   Starch_Yield
1   75.9
1   72.3
1   64.7
1   68.7
1   73.4
1   77.7
2   77.7
2   74.9
2   78.3
2   77.3
3   63.5
3   60.4
3   65.3
3   62.6
3   59.3
4   61
4   64
4   55.9
5   76.3
5   75.3
5   71.5
5   81

a) Perform an ANOVA test and report the F value and use 2 decimal places

b) Are the processes significantly different?

c) Which process(es) would you pick?

Solve using R studio and post code

Problem 2 For the same list as above, sort the list in such a way where the first set of numbers are ascending even and the second set of numbers are ascending odd. Your output should look like the following: [ 2, 4, 6, … 1, 3, 5 .. ]. The list is A = [ 6, 9, 0, 4, 2, 8, 0, 0, 8, 5, 2, 1, 3, 20, -1 ]

please use R for solving the questions

(e) Is multicollinearity a potential problem in this model?

(f) Construct a normal regression plot of residuals. Does there seem to be any problem with the normality assumption?

(g) Construct and interpret a plot of the residuals versus predicted response.

(h) Based on the above analysis, what is your recommended model?

[Hint: Use the lm commend in R to fit a regression equation.

Table B.4

Find the area of the region.
1) y=6x^2 and y= 8x-2x^2
2) y=1/2sin(pi x/6) and y=1/6x
3) y=x^3-4x and y=5x

#2 The Jacobsthal sequence is defined by J(1)=J(2)=1 and J(n)=J(n-1)+2J(n-2).  Use recursion to write a function that takes in a positive integer n and returns the nth Jacobsthal number.

>>> J(8)
85
>>> J(9)
171


#3 Use recursion to write a function that takes in a positive integer n and returns all n digit numbers containing only odd digits.

>>> f(1)
[1, 3, 5, 7, 9]
>>> f(2)
[11, 13, 15, 17, 19, 31, 33, 35, 37, 39, 51, 53, 55, 57, 59, 71, 73, 75, 77, 79, 91, 93, 95, 97, 99]
]
>>> f(3)
[111, 113, 115, 117, 119, 131, 133, 135, 137, 139, 151, 153, 155, 157, 159, 171, 173, 175, 177, 179, 191, 193, 195, 197, 199, 311, 313, 315, 317, 319, 331, 333, 335, 337, 339, 351, 353, 355, 357, 359, 371, 373, 375, 377, 379, 391, 393, 395, 397, 399, 511, 513, 515, 517, 519, 531, 533, 535, 537, 539, 551, 553, 555, 557, 559, 571, 573, 575, 577, 579, 591, 593, 595, 597, 599, 711, 713, 715, 717, 719, 731, 733, 735, 737, 739, 751, 753, 755, 757, 759, 771, 773, 775, 777, 779, 791, 793, 795, 797, 799, 911, 913, 915, 917, 919, 931, 933, 935, 937, 939, 951, 953, 955, 957, 959, 971, 973, 975, 977, 979, 991, 993, 995, 997, 999]


#5 Use recursion to write a function that takes in a positive integer n and returns all strings of zeros and ones of length n that do NOT have two consecutive ones.

>>>f(2)
['00','01','10']
>>>f(3)
['000','001','010','100','101']


#6 The Recaman sequence R(n) is defined to be 0 if n is 0.  For n>0 we define R(n) to be a(n-1)-n if a(n-1)-n is BOTH positive and not equal to R(0),R(1), ..., R(n-1).  Otherwise we define R(n) to be a(n-1)+n.  Use recursion to write a program to compute R(n).

>>> R(5)
7
>>> R(3)
6


#7 The Somos sequence is defined by S(n) = 1 if n is 1,2,3 or 4.  Otherwise it equals (S(n-1)S(n-3)+S(n-2)S(n-2))/S(n-4). Use recursion to write a program to compute S(n).

>>> [S(i) for i in range(1,10)]
[1, 1, 1, 1, 2, 3, 7, 23, 59]

PYTHON PLS

1) Create a function search_by_pos. This function only has one return statement. This function returns a set statement that finds out the same position and same or higher skill number. This function searches the dictionary and returns the same position and same or higher skill level. The function output the set statements that include the position only.

For example

input : dict = {'Fiora': {'Top': 1, 'Mid': 4, 'Bottom': 3},'Olaf': {'Top': 3, 'Mid': 2, 'Support': 4},'Yasuo': {'Mid': 2, 'Top': 5},'Shaco': {'Jungle': 4, 'Top': 2, 'Mid': 1}}

def search_by_pos(dict, 4):

#ONLY ONE RETURN STATEMENT ALLOWED

output : {'Mid', 'Support','Top','Jungle'}

2) Create a function search_by_rank this function calculates the average skill level for each champion and returns the champion's name by highest to the lowest average skill level. If two champions have the same average skill level, it must appear in increasing alphabetical order by name. This function needs to have only one return statement.

For example

input : dict = {'Fiora': {'Top': 1, 'Mid': 4, 'Bottom': 3},'Olaf': {'Top': 3, 'Mid': 2, 'Support': 4},'Yasuo': {'Mid': 2, 'Top': 5},'Shaco': {'Jungle': 4, 'Top': 2, 'Mid': 1}}

def search_by_rank(dict):

#ONLY ONE RETURN STATEMENT ALLOWED

output: ['Yasuo', 'Olaf', 'Fiora', 'Shaco']

1. A bond is 4% YTM, coupon 8%, term 5 years semi. It is sold in 2 years, calculate the holding period return. If the reinvestment rate is 3%, calculate the total return (MIRR), if it is callable in 2 years at 101, calculate the YTC.

E(Rp) = 12%, Rf = 2%, Бp = 4, βp = 1.5 Find the Sharpe and Treynor index.