[SOLVED] 代写 matlab graph Questions

Questions
On your PC go to your Y: drive (or any drive on your personal PC/Mac) and create a new folder called “matlabexam1920”. Then, go to the EC5200 Moodle page, download the data-set “prisons.csv”, and save this data-set in the folder that you have just cre- ated.
Now open matlab and create a script file named “matlabexam firstname lastname.m”, save this script file in the folder that you just created and make sure that matlab has this folder set as the current working folder.
Please answer ALL of the following questions.
(i) Open the data-set “prisons.csv” using the command “importdata”. The syntax is
the following:
myData = importdata(’Filename’, ’delimiter’, ’Nb of header lines’)
(You will lose marks if you don’t use the above command). (2 Marks)
You should now have a structure named “myData” that contains three elements: the raw data, the textdata and the column headers. The data-set contains information on prisoners in a certain district over time. The following syntax:
varname = myData.data(rows,cols)
allows you to create a new variable based on the “rows” and “cols” of the raw data that you specify.
(ii) Using the data in the first column of the raw data create a variable called “year”.
(5 Marks)
(iii) Create a variable called “ssize” and fill this with the sample size. What is the sample size? (5 Marks)
(iv) Now create the variables “inmates”, “time”, “time a” and “urate” using the correct columns in the raw data matrix. (5 Marks)
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The variable “year” defines the particular year of the prison sentence. The variable “time” describes the year and month of the prison sentence. The variable “time a” is equal to “time” plus 12 months (we won’t use this variable). The variable “urate” describes the unemployment rate at the year and month of the prison sentence.
(v) What is the mean number of inmates? Store this value in a variable named “minmate”. (5 Marks)
(vi) What is the mean unemployment rate? Store this value in a variable named “murate”. (5 Marks)
(vii) Create a new variable called “loginmate” that is equal to the log of the variable “inmates”. (5 Marks)
Next we would like to inspect the relationship between the number of inmates and the other variables in the dataset.
(viii) Create a scatter plot between “year” (x-axis) and “inmates” (y-axis). Label each axes and give the graph the title “EC5200 Exam Figure 1”. Save the figure as a .jpeg file. Comment on the relationship. (5 Marks)
(ix) Create a scatter plot between “urate” (x-axis) and “inmates” (y-axis). Label each axes and give the graph the title “EC5200 Exam Figure 2”. Save the figure as a .jpeg file. Comment on the relationship. (5 Marks)
Next we would like to estimate the impact of the unemployment rate on the number of prisoners (inmates). To do this we can run an OLS regression using the “fitlm” function with the following syntax:
lm = fitlm(X,y,’linear’)
(ix) Run the regression between “inmates” (Y) and “urate” (X). What is the slope coefficient β1? What is the intercept coefficient β0? Comment on the value of the slope, what does this number imply, why is it strange? (5 Marks)
(x) Plot the regression line [Hint: plot(lm)]. Label the axes and give the graph the title “EC5200 Exam Figure 3”. Save the figure as a .jpeg file. (5 Marks)
The last thing we would like to do is imagine that we live in a world where the function “fitlm” does not exist. Therefore if we want to run a regression we would need to write our own function that does this for us.
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(xi) Open a new script and create a function called “OLSestim”. We want the function to take the matrix of data “X” and the vector of data “y” as input variables and we want the function to return the estimated OLS coefficients (beta hat) and their standard errors (sigma hat) as outputs. The syntax on the script should therefore be the following:
function [beta hat, sigma hat] = OLSestim(X,Y) .
end
Save the function script in your created folder as “OLSestim.m”. (xii) The formula for βˆ (beta hat) is the following:
(5 Marks)
βˆ = (X′X)−1X′y
In your function script write the above formula [Hint: use the inv(·) function for
matrix inversion. The syntax will be: beta hat = …]. (5 Marks)
For our “OLSestim” function to calculate the standard errors, σ, of the OLS coefficients we first need to calculate the residuals: uˆ. To calculate the residuals we use the follow- ing formula:
uˆ = y − yˆ = y − X βˆ
(xiii) In the next line of your function script create a variable called “residuals” using the
above formula. Hint:
(xiv) The unbiased estimator of the error variance, σ2, is given by: σ 2 = uˆ ′ uˆ
n−k
residuals = Y – X*beta hat
(5 Marks)
Where uˆ are the residuals and (n − k) is the degrees of freedom. In the next line
of your function script create a variable called “df” which is equal to the degrees
of freedom. [Hint: degrees of freedom is the difference between the length of X and the length of beta hat.] (5 Marks)
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(xv) Using the residuals uˆ and degrees of freedom (n − k), in the next line of your function script create a variable “sigma sq” that is equal to the error variance. Hint: The syntax will be
sigma sq = (residuals’*residuals)/df
(xvi) The unbiased estimator of the standard errors is given by:
√
σ= σ2
(5 Marks)
Therefore, in the final line of your function script define the output variable “sigma hat” using the above formula. Hint: the syntax uses the “sqrt(·)” function for squared root. (5 Marks)
Now you have created your “OLSestim” function, save it, and return to your original exam “matlabexam firstname lastname.m” script file. In order to check that our function works we need to convert our existing data into the X and y variables.
(xvii) The y variable is just our variable “inmates” so you can leave this as is or create a variable “y = inmates”. Our X variable is the variable “urate”, however the X matrix needs to be of the form:
 1 urate(1,1) 
 1 urate(2,1)  X =  . .  ..
1 urate(n,1)
Create the X matrix by combining the the variable “urate” with a vector of ones of
length “samplesize”. (10 Marks)
(xviii) Now use your function to obtain the estimated OLS coefficients (beta hat) and
their standard errors (sigma hat), the syntax will be the following: [beta hat, sigma hat] = OLSestim(X,y)
Compare the outcome vector “beta hat” with the estimated coefficients you ob- tained using the “fitlm” function (i.e. “lm.coefficients”) – if your function worked correctly these values should be the same. (10 Marks)
END
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[Total 100 marks]