Consider the following daily time series representing the number of clients visiting the Small Business Development Center over the previous 10 days.

Step 1 of 2: What is the Simple Exponential Smoothing Forecast for day 11 (t = 11) assuming that the smoothing constant, alpha = 0.2?
Round to 2 decimal places.

Step 2 of 2: What is the Simple Exponential Smoothing Forecast for day 11 (t = 11) assuming that the smoothing constant, alpha = 0.75?
Round to 2 decimal places.

You wish to estimate as precisely as possible the slope β1 in the simple linear regression model yi = β0 + β1xi + ei , i = 1, . . . , 4. Each pair of observations (xi , yi) costs $ 1:00 and your budget is $ 4:00. A data analyst proposes that you consider one of the following two options:

(a) Make two y-observations at x = 1 and a further two at x = 4;

(b) Make one y-observation at each of the points x = 1; 2; 3 and 4.

Which of the two options would give you the most bang for your bucks? Show the relevant calculation to justify your choice.

CAPM and expected​ returns..

a.  Given the following​ holding-period returns, compute the average returns and the standard deviations for the Zemin Corporation and for the market.

b.  If​ Zemin's beta is 1.88 and the​ risk-free rate is 7 percent, what would be an expected return for an investor owning​ Zemin? ​

(Note: Because the preceding returns are based on monthly​ data, you will need to annualize the returns to make them comparable with the​ risk-free rate. For​ simplicity, you can convert from monthly to yearly returns by multiplying the average monthly returns by​ 12.)

c.  How does​ Zemin's historical average return compare with the return you believe you should expect based on the capital asset pricing model and the​ firm's systematic​ risk?

Question 2 The rest of the questions deal with the Motor Trend Car and Sport data from 1974

# It is famous dataset called mtcars comes built in to R. Use the line of code below

# to familiarize yourself with it head(mtcars)

## mpg cyl disp hp drat wt qsec vs am gear carb

## Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4

## Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4

## Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1

## Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1

## Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2

## Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1

Question 2a # how many observations are there in this data set?

Question 2b # plot a histogram showing the frequencies of the "cyl" column # as always, make sure the plot is properly labeled.

Question 2c # which car has the highest "qsec"? # which car has the highest "mpg"?

Question 2d The next two questions are great practice for your final project! 1 # plot a scatter plot of mpg vs qsec. Are the variables correlated? If so, are they # negatively correlated or positively correlated?

Question 2e # plot a scatter plot of mpg vs disp. Are the variables correlated? If so, are they # negatively correlated or positively correlated?

Calculate the directional derivative of f(x,y,z)=x(y^2)+y((1-z)^(1/2)) at the point P(1,−2,0) in the direction of the vector v = 5i+2j−k. (a) Calculate the directional derivative of f at the point P in the direction of v. (b) Find the unit vector that points in the same direction as the max rate of change for f at the point P.

(a) Determine the inverse Laplace transform of F(s) =(2s−1)/s^2 −4s + 6
(b) Solve the initial value problem using the method of Laplace transform. d^2y/dx^2 −7dy/dx + 10y = 0, y(0) = 0, dy/dx(0) = −3.
(c) Solve the initial value problem:
1/4(d^2y/dx^2)+dy/dx+4y = 0, y(0) = −1/2,dy/dx(0) = −1.

Use Theorem 3.5.1 to find the general solution to each of the following systems. Then find a specific solution satisfying the given boundary condition.

a. f1′=2f1+4f2,f1(0)=0 f 2′ = 3 f 1 + 3 f 2 , f 2 ( 0 ) = 1

c. f1′= 4f2+4f3 f2′= f1+f2−2f3 f 3′ = − f 1 + f 2 + 4 f 3 f1(0) = f2(0) = f3(0) = 1

Question 1 (1 point)

What is the range of the following: 18, 20, 14, 48, 51, 70

Round to 2 decimal places as needed.

Your Answer:

Question 1 options:

Question 2 (1 point)

What is the range of the following: 32, 69, 16, 13, 32, 32

Round to 2 decimal places as needed.

Your Answer:

Question 2 options:

Question 3 (1 point)

What is the range of the following: 16, 72, 51, 41, 37, 12

Round to 2 decimal places as needed.

Your Answer:

Question 3 options:

Question 4 (1 point)

What is the standard deviation of the following: 49, 39, 19, 15, 39, 38

Round to 2 decimal places as needed.

Your Answer:

Question 4 options:

Question 5 (1 point)

What is the standard deviation of the following: 23, 31, 47, 34, 40, 28

Round to 2 decimal places as needed.

Your Answer:

Question 5 options:

Question 6 (1 point)

What is the standard deviation of the following: 13, 50, 37, 42, 13, 18

Round to 2 decimal places as needed.

Your Answer:

Question 6 options:

Scheme Programming - Racket R5RS

Longest Non-Decreasing Subsequence

You will write two Scheme functions that compute a longest non-decreasing subsequence from a list of numbers. For example, if you type

> (lis '(1 2 3 2 4 1 2))

you might get

(1 2 3 4)

Note that there may be more than one longest non-decreasing subsequence. In the above example, your program might also find (1 2 2 4) or (1 2 2 2).

You should concentrate first on simply getting a solution working. One possibility is simple exhaustive search:

for i := n downto 1, where n is the length of the input list

    for all i-element sublists s of the input list

      if s is a non-decreasing sequence of numbers

         print s and quit

Unfortunately, this algorithm is inefficient. The number of distinct sublists of a given list is 2ⁿ (to generate a sublist, we have two choices -- include or exclude -- for each of n elements).

Once you have a simple version running using the above algorithm, your next task is to find a polynomial-time solution.

To avoid typing long lists at the interpreter line, I suggest you create a few sample arguments in a file, say my_lists.rkt. You can create those definitions in DrRacket's definition window and save them in file my_lists.rkt. For example, if my_lists.rkt may contain definitions

(define list1 '(1 2 3 2 4 1 2))

(define list2 '(2 4 3 1 2 1))

you can call

> (lis list1)

and

> (lis list2)

• Write two functions, lis_slow, which implements the pseudocode above and lis_fast, which implements a polynomial solution. Both lis_slow and lis_fast consume a list of numbers as arguments and produce a list as a result, as shown in the lis examples above. Include functions lis_slow and lis_fast in your lis.rkt file.
• You are not allowed to use imperative features of Scheme. Do not use side-effecting functions (i.e., functions with exclamation point in their names such as set!), sequencing, iteration (e.g., do, for-each) or vectors. Do not use input/output mechanisms other than the regular read-eval-print loop. (You may find imperative features useful for debugging. That's ok, but get them out of your code before you turn anything in.) Code the algorithms in terms of the purely functional subset of Scheme we have covered in class, however you are allowed to use some additional built-in list operations, e.g., reverse, list-ref, etc.
• You must comment your code! You are required to write comments using the style described here.