R programming interpretation

3.
a.
The model is adequate because the multiple r-squared score is 0.9797. It means that the model used is 97.97% compatible with the heart data.
b.
X1 is the independent variable and for our case it is the biking variable
X2 is the controlling variable and for the case of these assignment it is the smoking variable.
Y is the dependent variable and four our case it is the heart disease variable.
ε is the error variable
c.
The model is adequate because of the high multiple r-squared score of 0.9796. It means that the model is 97.96% suitable to be used investigate the impact of biking and smoking on the heart disease occurrence.
d.
The validation that can be undertaken is as follows:-
• Determining linearity
• Finding homoscedasticity
• Determining presence or absence of multicollinearity
• Independence and normality of errors
I can validate the following:-
• Finding homoscedasticity
• Finding multicollinearity scores
e.
The difference between the two tables are sum sq, mean sq and f value.
The first table explains that point increase in biking causes a 9090.6 impact on heart disease total sum while the second table shows that point increase in biking causes a 9183.8 on heart disease total sum.
The first table shows that a point increase in smoking causes 1086.0 impact on heart disease. The second table shows that a point increase by both smoking result in 992.7 impact on heart disease.
f.
SOURCE D.F S.S M.S F VALUE
BIKING 1 9090.6 9090.6 21251.7
RESIDUAL 495 211.7 0.4 -
TOTAL 496 9302.3 9091.0 21251.7
4.
a.
A balanced design occurs where all the treatment groups have equal number of experiment units.
Yes the experiment is balanced
b.
The 1 graduation group performed better based on all training methods and proficiency test while graduation group 3 performed the least.
c.
The first model is better as compared to the second model. This is because the first model has a lower sum square residual of 47 as compared to the second model with sum square residual of 64.33. A point increase in graduation group has a 152.33 impact on the proficiency score while a point increase in the method of training as a 849.33 impact on proficiency score of students.
d.
The Tukey HDS is suitable for the data because it is used to assess the significant difference between pairs of groups taking into consideration that both training methods and graduations exist in groups.
e.
The training methods are suitable for the proficiency scores obtained based on the Tukey HDS. The training method p value is less that the 0.05 significant value thus the null hypothesis is rejected. The 2-1 graduation group p value is greater than the significant value thus fail to reject the null hypothesis. The 3-1 and 3-2 graduation groups p value is less than 0.05 significant value thus reject the null hypothesis.

Intermediate Econometrics

1. (20 points total) A research team wants to know how much does education affect wage rates. The team collected 1000 observations on hourly wage rates, education and other variables from the 2008 Current Population Survey. Wage is measured in earnings per hour (WAGE) and education (EDUC) denotes years of schooling. The following equation is estimated by least squares. The estimates and standard errors are
(WAGE) ̂ = 6.08 + 0.07〖EDUC〗^2 (1.02) (0.005)
(a) (5 points) Sketch the estimated regression function for EDUC= 0 to 20 years (in 5-yearly intervals).
(b) (5 points) Predict the wage of a person with 10 years of schooling.
(c) (5 points) Using each model, find the marginal effect of another year of experience on the expected worker rating for a worker with 10 years’ experience.
(d) (5 points) Construct a 95% interval estimate for the marginal effect found in part c.
  2. (30 points total) The life-cycle pattern of wages can be explained by MODEL 1 below
MODEL 1
Wage=β_1+β_2 EDUC+β_3 EXPER+β_4 EXPER^2+ e (1)
The STATA output from estimating the equation using 1000 observations is
Source | SS df MS Number of obs = 1000 -------------+------------------------------ F( 3, 996) = 104.25 Model | 34973.3163 3 11657.7721 Prob > F = 0.0000 Residual | 111382.245 996 111.829563 R-squared = 0.2390 -------------+------------------------------ Adj R-squared = 0.2367 Total | 146355.561 999 146.502063 Root MSE = 10.575 ------------------------------------------------------------------------------ wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | 2.277391 .1394284 16.33 0.000 2.003784 2.550999 exper | .6820989 .1048198 6.51 0.000 .476406 .8877919 exper2 | -.0100907 .0018645 -5.41 0.000 -.0137495 -.006432 _cons | -13.43025 2.028486 -6.62 0.000 -17.41084 -9.449648 ------------------------------------------------------------------------------
The variance-covariance matrix is
educ exper exper2 _cons
educ .01944028
exper -.00021758 .01098718
exper2 .00001547 -.00018926 0.000003476
_cons -.21550584 -.12402316 .00182269 4.1147573
(a) (5 points) After how may years of experiece do wages start to decline? (Express your answer in terms of β’s?
(b) (5 points) What is the marginal effect of education on wages? Is it statistically significant at 5%?
(c) (5 points) Find the elasticity of wages with respect to experience when EXPER = 4. Is it statistically significant?
(d) (5 points) Find the 95% confidence interval for the marginal effect of experience on wages when EXPER = 4.
  After estimating Eq. (1), the residuals are obtained and plotted in the histogram below.
(e) (5 points) What is the reason for assuming that the error term e is normally distributed? Do you have evidence that this is true?
(e) (5 points) Another possible model of wages is
MODEL 2
log⁡(Wage)=β_1+β_2 EDUC+β_3 EXPER+β_4 EXPER^2+ e (2)
Carefully explain, how would you evaluate if Model 1 or Model 2 is a better fit of the data?
3. (15 points total) Consider the model
y=β_1+β_2 x_2+ β_3 x_3+e
and suppose that application of least squares to 63 observations on these variables yields the following results ((cov(b)) ̂ denotes the estimated variance-covariance matrix.
[■(b_1@b_2@b_3 )]=[■(2@3@-1)], (cov(b)) ̂=[■(3&-2&1@-2&4&0@1&0&3)], σ ̂^2=2.5193 R^2=0.9
(a) (5 points) Test the hypothesis that β_2=0 using a 95% confidence interval.
(b) (5 points) Use a t-test to test the hypothesis H_0:β_1+2β_2=5 against the alternative H_1:β_1+2β_2≠5 at 10% significance level.
(c) (5 points) Use p-values to test the hypothesis H_0:β_1-β_2+β_3=4 against the alternative H_1:β_1-β_2+β_3≠4 at 5% significance level.
  4. (10 points total) Consider a model of wheat yield that allows for the yield response to be different for the three different periods
y=β_1+β_2 t+ β_3 rg+β_4 rd+β_5 rf+e (3)
Where
y is the wheat yield in tonnes per hectare,
t is the trend term to allow for technological change,
rg is rainfall at germination (May-June),
rd is rainfall at development stage (July-August), and
rf is rainfall at flowering (September- October).
You estimated this model using 48 annual observations on a number of variables related to wheat yield in the Toodyay Shire of Western Australia, for the period 1950-1997. The unit of measurement for rainfall is centimeters.
The estimated results are below
Test the hypothesis that the response of yield to rainfall is the same irrespective of whether the rain falls during germination, development, or flowering. The results of the restricted model are:
5. (15 points total) Let us investigate if taking econometrics affect starting salary. Let SAL = salary in dollars, GPA= grade point average on a 4.0 scale (the higher one’s GPA is, the better is his/her academic performance), METRICS = 1 if student took econometrics and METRICS = 0 if otherwise. Using a sample of 50 recent graduates, we obtain the estimated regression
(a) (5 points) Interpret the estimated equation.
(b) (5 points) How would you modify the equation to see whether double international students had a higher starting salaries than local students?
(c) (5 points) How would you modify the equation to see if the value of econometrics was the same for international and local students?
END OF EXAMINATION.
STATISTICAL TABLES FOLLOW.

MA Applied Imagination

MA Applied Imagination will help you become a problem-finder and change-maker. You will apply your imagination and question existing assumptions in the creative disciplines. This course is part of the Culture and Enterprise programme.
Why choose this course at Central Saint Martins
Festival of Applied Imagination: You will participate in the course festival, presenting your final project outcomes to your peers, professionals and to the public.
Interdisciplinary approach: You will work collaboratively through the interdisciplinarity and cultural cross-fertilisation that the Culture and Enterprise programme provides.
Experienced feedback: You will be given the opportunity to investigate your ideas through a series of interventions and obtain feedback from end users and key practitioners.
Independent research: The course structure allows for an extended period of independent research. You will be encouraged to use this for testing projects with external partners and stakeholders. This feature will develop your strengths in self-directed study and creative work, as well as building skills in creative networking.

Confidential

1. i.
I support the application of AR (2) by Peter because it increases the user knowledge and information. The application of AR (2) is a disadvantage because quite expensive for everyday application and it is not accessible to small businesses.
ii.
When describing the process, it is important to study both the ACF plot and the PACF plot together. It is anticipated that the ACF plots for AR (2) would show a gradual decrease, but the PACF plots are anticipated to show a sudden reduction after the first substantial delays. The ACF should show a sudden decline after a certain number of delays (q), while the PACF should show a geometric or progressive decline in trend for the ACF and PACF plots to indicate the opposite of what we expect to see in an MA process. In other words, the ACF should show the reverse of what we expect to see in an MA process.
iii.
The proposed Elizabeth’s MA (1) is suitable because it’s smooth nature and lower probability of producing false signal. The smoothness allows the users of the MA (1) to clearly identify trends in the market. The lower probability of false signal allows its users to be in a better position to identify opportunities in the market.
iv.
Model one
Xt = 0.77Xt−1 + 0.21Xt−2 +Zt
X – 0.98x = Z
0.02 (0.8661) = Z
= 0.0173
Model two
Yt = Zt −0.19Zt−1, where Yt = Xt −Xt−1
Thus:-
Zt −0.19Zt−1 = Xt −Xt−1
z = 0.81(0.8806)
= 0.7133
v.
Model one
Using the value obtained 0.0173 and the aic as follows:-
=0.0173 * 547.89
= 9.4785
Model two
Using the obtained value 0.7133 and the aic as follows:-
= 0.7133 * 543.46
= 387.65
vi.
We are analyzing this specific variable with the help of a model called ARIMA (1,1,1), which has both an AR and an MA term. One of the possible explanations for the linear trend in the data is a first difference.
2.
i.
Xt = 6 – 0.7 + 0.5 + 0.9
= 6.7
ii.
iii.
Let k be 2 which is equal or greater to 2
3.097 = 0.7p2-1
0.7P1 = 3.097
P1 = 4.4243
iv.
The ARIMA (1, 1) model is better than the AR (1) model based on the inclusion of 0.5Zt−1 in the ARIMA (1, 1) model. The ARIMA (1, 1) model performs better in short period of time as compared to AR (1) that doesn’t perform better in short period.
3.
i.
Xt = 26+0.5Xt−1 −0.8Xt−2 +Zt +0.6Zt−2 −0.4Zt−3
t = 300
Thus:-
X300 = 26+0.5X300−1 −0.8X300−2 +Z300 +0.6Z300−2 −0.4Z300−3
X300 = 26+0.5X299 −0.8X298 +Z300 +0.6Z298 −0.4Z297
ii.
The model in long-term profitability is 20 when l → ∞ because of the factor 1.22.
iii.
The increament from 300 to 301 is subjected to an increase and so forth:-
X301 = 1.2 + 1(0.3) = 1.5
X 302 = 1.2 + 2(0.3) = 1.8
X 303 = 1.2 + 3(0.3) = 2.1
iv.
The two-step-ahead forecast error is 2(0.3) = 0.6 and the variance is 0.3

The world of content writing

Content writing is the ability to develop content about a specific topic from scratch. Content writing allows a content writer to be an artist in providing a vivid description to readers regarding a certain event. The world of content writing has been in existence over a long period of time. This is because new content is always required thus increasing the demand for content writing. As a result hiring content writers is an important vice of ensuring that an organization continues to provide new contents to the consumers. The content writing provides a description thus allowing readers of the content to have a solid understanding of an event.

The process of content writing is important to all content writers across the world. This is because all content writers make use of similar process thus ensuring that the content being developed is of high quality. The process of coming up with high quality content to suit the needs of the consumers is important. This is because it allows for the organization to be able to maintain their consumers (readers). It also provides an important source of information for the organization. As a result content writing is an important field to organization aiming at maintaining their online presence.

Optimization Math 1010 Project

Background Information:
Linear Programming is a technique used for optimization of a real-world situation. Examples of optimization include maximizing the number of items that can be manufactured or minimizing the cost of production. The equation that represents the quantity to be optimized is called the objective function, since the objective of the process is to optimize the value. In this project the objective is to maximize the audience of a small business.
The objective is subject to limitations or constraints that are represented by inequalities. Limitations on the number of items that can be produced, the number of hours that workers are available, and the amount of land a farmer has for crops are examples of constraints that can be represented using inequalities. Manufacturing an infinite number of items is not a realistic goal. In this project some of the constraints will be based on budget.
Graphing the system of inequalities given by the constraints provides a visual representation of the possible solutions to the problem. If the graph is a closed region, it can be shown that the values that optimize the objective function will occur at one of the "corners" of the region.
The Problem:
In this project your group will solve the following situation:
Elizabeth Bailey is the owner and general manager of Princess Brides, which provides a wedding planning service in Southwest Louisiana. She uses radio advertising to market her business. Two types of ads are available -- those during prime time hours and those at other times.
Each prime time ad costs $390 and reaches 8,250 people, while the offpeak ads each cost $240 and reach 5,100 people. Bailey has budgeted $1,800 per week for advertising.
Based on comments from her customers, Bailey wants to have at least 2 prime time ads and no more than 6 off peak ads.
Your goal is to figure out how many of each ad should be aired and what is the total reach of your audience.
Modeling the Problem:
Let x be the number of prime ads that are made and y be the number of non-prime that are made.
1. Write down a linear inequality that models how the cost of ads will be kept within budget.
2. Recall that she wants least 2 prime time ads and no more than 6 off peak ads. Write down two linear inequalities to model these constraints.
3. There are two more constraints that must be met. These relate to the fact that it is impossible to buy a negative number of ads. Write the two inequalities that model these constraints:
4. Next, write down a linear equation that models the total reach/audience of the ads. This is the Objective Function for the problem.
𝑅𝑅 ��(�𝑥𝑥, �𝑦𝑦 �) = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅ℎ 𝑜𝑜𝑜𝑜 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴
You now have five linear inequalities and an objective function. These together describe the situation. This combined set of inequalities and objective function make up what is known mathematically as a linear programming problem. This is typically written as a list of constraints, with the objective function last.
5. To solve this problem, you will need to graph the intersection of all five inequalities on one common x,y-plane. Do this on the grid below or you may use your own graph paper or graphing software if you prefer. Let the bottom left be the origin, with the horizontal axis representing x and the vertical axis representing y. Be sure to:
a. Label the axes with appropriate numbers and verbal descriptions
b. Label your lines as you graph them.
The shaded region in the graph is called the feasible region. Any (x, y) point in the region corresponds to a possible number of peak and off-peak ads that will meet all the requirements of the problem. Your region should have three corners or vertices.
6. Generally, to find which number of each type of ad that will maximize the audience you would evaluate the objective function R for each of the vertices you found. But notice that two of the vertices would have decimals and we can’t purchase a decimal number of ads. So instead, let’s list out all possible integer ordered pairs INSIDE the shaded area. (Hint: you should have 10 ordered pairs). Evaluate all 10 of the possible integer pairs that fall within the shaded region for the objective function R. Determine which ordered pair gives you the maximum audience/reach? Ordered Pair Evaluate for #4: R(x,y) = Audience Reached at Ordered Pair
Your goal is was figure out how many of each ad should be aired. Write one to two sentences describing how many of each item should be purchased to produce the greatest reach. Include the audience number that will be reached in your description.
Reflective Writing – Please type your answer/reflection on a separate sheet of paper and submit it with the pages above.
Did this project change the way you think about how math can be applied to the real world? Write at least one paragraph stating what ideas changed and why. If this project did not change the way you think, write how this project gave further evidence to support your existing opinion about applying math. Be specific.

Academic Writers Galore

Academic writing has been on the rise over the past one decade due to embracing of technology. Technology has allows scholars and students alike to hire academic writers to tackle their tasks at a cost effective amounts. Academic writers has allowed students to continue working while continuing with their academic endeavors. Academic writing allows students, researchers and scholars alike to access quality content written within a limited period of time. They can further use the materials as a reference to further explore the topic of study. Academic writers help students through pointing them in the correct path thus reducing the hassle involve while undertaking studies.

The academic writing allows academic writers around the globe to sell their skills in different online platforms. As a result academic writers are able to make a living for themselves while providing services to consumers. The academic writing platform can be easily accessed by the students and academic writers alike. The platforms allows the students to directly select a writer from a large pool of academic writers. The students are also allowed to communicate directly with the writers thus ensuring that information exchange between the two parties is guaranteed. As a result the quality of service offered to the consumers is high.

The concept of academic writing has been in existence for many years and it has been fueled up by easy access of technology. The widespread of academic writers around the globe has given rise to specialization. This is where academic writers have specialized based on niches that they are able to produce high quality content to their consumers.