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Hello:
Please find a pdf file. I ONLY NEED HELP WITH THE LAST QUESTION that is a Statistics based question (Regression Statistics) and would appreciate an answer to question 10 below.
Deadline: During the next 12 hours.
MFin Maths and Stats Precourse Test Questions
The approximate number of marks for each question is indicated in square brackets below the
question number.
1.
[3]
Find the derivative dy/dx of:
x
xx
y
ln
43 2
.
2.
[4]
Find the following integral:
2
0
dxxe x .
3.
[10]
What are the maximum and minimum values of the function
xxexf for x ≥ 0 ?
4.
[3]
Find the partial derivative with respect to 1x of the function:
2
3
2
211
321
34
,,
x
xxx
xxxfy
.
5.
[10]
Minimise 2221
2
1 42 xxxxy subject to the constraint 121 xx .
6.
[10]
Find the Taylor Series of f = ln(x) about x=1.
7.
[10]
Find the solution of the differential equation:
5.103.0 x
dt
dx
where the value of x at time 0 is 60.
8.
[10]
Let
3 ayx
422 yx
Write these equations in matrix form bxA .
Find A2.
Does a solution to the equations for x and y exist when a = 1?
9.
[20]
The price of a specific CD by Band X is observed in 10 Cambridge stores on the same
day. The data obtained, given in pounds sterling, are shown below:
8.00; 10.40; 10.60; 10.80; 11.00; 11.00; 11.30; 11.80; 12.00; 12.00
Assuming that Cambridge typifies the country in terms of prices, estimate the mean UK
price and the variance, and set up a 95% confidence interval for the mean. What other
assumptions do we need to make?
You may find some of the following two-tailed 5% critical statistics useful:
Standard Normal Z = 1.96; t8 = 2.306, t9 = 2.262, t10 = 2.228, t11 = 2.201
10.
[20]
Consider the following data on birth rates and GNP. The objective is to explain
variations in birth rate across countries.
Birth rate (Y) GNP(X)
Bangladesh 47 1
40
Tanzania 47 280
Sierra Leone 46 3
20
Sudan 47 380
Kenya 55 420
Indonesia 35 5
30
Panama 30 19
10
Chile 25 25
60
Venezuela 35 4220
Turkey 33 1540
Malaysia 31 1840
Nepal 44 1
50
Malawi 56 200
Argentina 20 2560
A graph of the data and a regression analysis carried out using Excel are shown below.
0
10
20
30
40
50
60
0 1000 2000 3000 4000 5000
GNP
B
ir
th
R
at
e
Regression Statistics
Multiple R 0.730643
R Square 0.533839
Adjusted R Square 0.494992
Standard Error 7.832454
Observations 14
ANOVA
df SS MS F Significance F
Regression 1 843.0462048 843.0462 13.74218 0.002997
Residual 12 736.1680809 61.34734
Total 13 1579.214286
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 47.18212 2.972809907 15.87122 2.03E-09 40.70493 53.65932
GNP -0.00643 0.001733241 -3.70704 0.002997 -0.0102 -0.00265
(a) What would the correlation coefficient be?
(b) Is the slope coefficient significantly different from zero? Explain why.
(c) Comment briefly on the value of this exercise and any weaknesses it has.
