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Question Description

Question in Business Statistics

Every year, millions of high school students apply and vie for acceptance to a college of their choice. For many students and their parents, this requires years of preparation, especially for those wishing to attend a top-ranked college. In high schools, students usually work with college advisors to research different colleges and navigate the admissions process.

Elena Sheridan, a college counselor at Beachside High School, is working with 14 students who are interested in applying to the same selective four-year college. She is asked by her school principal to prepare a report that analyzes the chances of the 14 students getting accepted into one of the three academic programs. In a database of past college applicants available to counselors at Beachside High, predictor variables include the student’s high school GPA, SAT score, and the Male, White, and Asian dummy variables that capture the student’s sex and ethnicity. Elena also wants to know whether or not the parents’ education can be a predictor of a student’s college acceptance and plans to include the education level of both parents in her analysis.

Based on her conversation with college counselors at other high schools, she believes that high school students with a GPA of 3.5 or above have a much higher chance of getting accepted into a selective college. She also thinks that SAT scores of at least 1,200 substantially increase the chance of acceptance. To test these anecdotal assumptions, Elena wants to convert the GPAs and SAT scores into the categories corresponding to these thresholds. In addition, the database has a target variable indicating whether or not the past applicant was accepted to the college.

Develop the naïve Bayes classification model and create a report that presents an analysis of the factors that may influence whether or not a high school student is admitted to a selective four-year college. Predictor variables should include the applicant’s sex, ethnicity, parents’ education levels, GPA, and SAT scores. Transform the GPAs and SAT scores into appropriate categorical variables. Make predictions whether or not each of the 14 high school students at Beachside High in the College_Admission_Score worksheet will be admitted.

High school students work hard to excel academically and set themselves apart with extracurricular achievements. Getting into the right college and choosing the right major can help start them out on a successful professional career.

The college admissions data set that is available to Beachside High School counselors includes records of past students who had applied to a selective four-year college that has three academic units: School of Arts and Letters, School of Business and Economics, and School of Mathematics and Sciences. The data set is used to develop classification models based on a naïve Bayes algorithm to predict whether or not the 14 high-achieving students at Beachside High will be admitted to any of the three academic units at the college.

The 14 current students are the top students in their graduating class. However, because the admission process can be highly competitive, some of these students might not get admitted to the college they wish to attend. Moreover, different academic programs may have different admission criteria. As a result, a naïve Bayes classification model is developed for each of the three academic schools based on the following variables: parents’ education, high school.

GPAs, SAT scores, and the male, white, and Asian indicators. Because the naïve Bayes algorithm requires that all predictor variables are categorical, GPAs and SAT scores are converted into binary values where GPAs that are at least 3.50 are denoted as 1, 0 otherwise, and SAT scores that are at least 1,200 are denoted as 1, 0 otherwise. A summary of the students’ demographic and academic information is as follows.

Of the 14 students, eight of them are female. Four students are of Asian descent, and six are nonwhite.
The average high school GPA and SAT score of the 14 students are 3.64 and 1,261, respectively.
Nine students have a current GPA of 3.50 or higher, and 10 students scored at least 1,200 on the SAT exam.
All but three students have at least one parent who completed a four-year college degree.
Even though the current students have not decided which academic program they want to pursue, most of them express an interest in the School of Arts and Letters. The data set has 6,964 records of past applicants to this program, which are partitioned into training, validation, and test data sets. Based on the test data set, the naïve Bayes model for the School of Arts and Letters has an overall accuracy rate of 75.81%. The specificity and sensitivity rates are 84.65% and 48.83%, respectively.

A summary of performance measures of the classification models for the three academic schools is shown in Table 9.10. The naïve Bayes model predicts that only four of our 14 top students will be admitted to the School of Arts and Letters. This program appears to be the most selective of the three academic units. The scoring results of the 14 students for each of the three academic schools are presented in Table 9.11.

TABLE 9.10 Performance Measures of Naïve Bayes Classifiers
The School of Business and Economics is also a popular choice among the current students. The data set has 4,103 records of past applicants to this program, which are partitioned into training, validation, and test data sets. The accuracy, specificity, and sensitivity rates based on the test data are 77.44%, 83.20%, and 67.86%, respectively. The model predicts that six out of the 14 students will be admitted into this program.

A similar naïve Bayes classifier is developed based on the 6,272 records of past applicants to the School of Mathematics and Sciences. As presented in Table 9.10, the accuracy, specificity, and sensitivity rates based on the test data are 76.24%, 79.81%, and 69.19%, respectively. Based on the scoring results, six out of the 14 students are likely to be admitted into this program. These are the same six students that the previous model classifies as likely to be admitted into the School of Business and Economics.

Based on the overall accuracy rate, the naïve Bayes classifiers perform reasonably well. The lift ratios and the decile-wise lift chart also indicate that the naïve Bayes classifiers are more effective than a baseline random model. As shown in Table 9.10, the lift values of the first decile of the three models are above 2.0, and the AUC values are around 80%. However, compared to other performance measures, the sensitivity rate of the models is relatively low, especially for the School of Arts and Letters. This may be because the schools also use qualitative information that is not captured in the database, making it difficult to correctly classify all of the past applicants who were admitted to the college (i.e., identifying true positive cases). The qualitative factors that are relevant to the admission process include letters of recommendations, written essays, and, for the School of Arts and Letters, a student’s artwork.

Table 9.11 presents the scoring results of the 14 current students. In general, the only students who are likely to be admitted into any of the three academic programs are those who maintain a GPA of at least 3.50 and score 1,200 or above on the SAT exam. Out of the 14 students, only six of them meet both criteria. A high GPA or a high SAT score alone is not likely to result in an acceptance to the college.

These data-driven results confirm the anecdotal intuition that a GPA of 3.50 and an SAT score of 1,200 are the minimum thresholds that students at Beachside High need to achieve in order to be admitted into a more selective college or university. Moreover, the School of Arts and Letters appears to be more selective than the other two schools. Only four of the six students with a GPA above 3.50 and an SAT score above 1,200 are likely to get accepted into this program. With this information, it is advised that some of the 14 students wishing to attend the School of Arts and Letters apply to additional colleges and universities with a similar degree program as a back-up plan.

TABLE 9.11 Prediction Results for the 14 Students

MA Level Cultural Diversity Paper
The purpose is to assist students in exploring and understanding information about a non-dominant or minority group in Canada and how they may bring this knowledge into their counselling work clients who may be in this group. Please follow the instructions below and ensure that you divide the paper based on the following headings mentioned below in the instruction details (6 A, B, C & D)

Instructions Write a paper about counselling a specific cultural group that is clearly identified in the literature as a cultural group and that is in Canada. Your paper should be approximately eight (8) double-spaced pages long (or approximately 2000 words, +/- 100 words), excluding the cover page and the reference list.
Please provide at least eight (8) recent (last 7 years), peer-reviewed sources and a maximum of 16 recent, peer-reviewed sources. Remember that the course textbooks are not peer-reviewed sources. If you cite from course texts, make sure that you correctly cite the original source and not the editor of the book. Title the report "Counselling X," where X is the specific cultural group being reported on and focus on cultural groups in Canada. You must include Canada or Canadian in the title.
Examples of appropriate titles are: -Counselling Turkish-Canadian Clients, -Counselling Greek-Canadian Clients, -Counselling Eastern-European Canadian Clients -Counselling Indigenous Youth in Canada Papers on counselling a specific Indigenous group of bands (such as the Inuit, prairie dwellers, youth, women, urban dwellers, adolescents living on reserves, etc.) are encouraged, as are reports on an Indo-Canadian or Chinese-Canadian subculture, such as children, adolescents, or women. Make sure to clearly define the group and delineate the age range for groups such as youth, children, or adolescents. Reports on other specific groups or subcultures are also welcome. Examples include: -Counselling Muslim Immigrant Clients in Canada, -Counselling Syrian Refugees in Canada, -Counselling Members of the Canadian Armed Forces, -Counselling Bicultural Adolescents in Canada, -Counselling Interethnic Couples in Canada, and -Counselling Deaf Clients in Canada. Do not write on a topic that is too general such as Counselling Asian, Latino, African, European, Indigenous, Refugee, or Immigrant Clients in Canada. 6. Include a brief introduction as well as a brief conclusion with a maximum of about 100 words for each. Do not include an abstract. Complete these four sections. A. Socio-cultural and demographic background (20%) In this section, include descriptive information about the specific cultural group that you have researched, such as demographics, history, social and cultural customs, traditions, belief system and values, as well as epidemiological data on the prevalence of certain conditions, if such data exist. Make sure to be as specific as possible in your description. For example, if you write about youth in a particular group, make sure to define what age range you mean and that researchers have noted. Include at least two (2) recent (last seven years), peer-reviewed sources.
You may use information from required course readings and remember that the course texts are not peer-reviewed. Write about 450 words for this section. B. Counselling strategies (30%) In this section, include information about how you would conceptualize a presenting concern or concerns brought into counselling by someone in the cultural group. For illustrative purposes, you may develop a hypothetical client. The focus in this section is on considerations of therapeutic alliance and experiences that a client in this group may have had such as intergenerational trauma, personal trauma such as adverse childhood experiences, or experiences that may have contributed to them becoming migrants who are now refugees or immigrants in Canada, experiences of oppression and/or marginalization or anything that you believe may have contributed to them seeking counselling. You may make references to the theoretical material covered in the course, such as influences of individualism and collectivism, models of cultural identity formation, acculturation, or any other topic area that you think is relevant to the cultural group. Include at least three (3) recent (last seven years), peer-reviewed sources. You may use information from required course readings and remember that the course texts are not peer-reviewed. Look for sources that are about the particular cultural group in Canada. If you cite sources that are about the cultural group in other countries than Canada, explain how you think the information fits for the cultural group in Canada. Remember to include your voice in what you are writing and note what you think about the research that you have read about the cultural group. Write about 700 words for this section. C. Counselling interventions (20%) In this section, address specific practical techniques that you believe would be appropriate and effective in working with clients in the cultural group. Include at least three (2) recent (last seven years), peer-reviewed sources. Describe which interventions you may already utilize or would most likely utilize when you work from clients in the cultural group and why you think that they would be effective. Write about 450 words for this section D. Directions for future research (10%) In this section, identify existing gaps in the current research on and knowledge of diversity and cross-cultural counselling theory and practice related to the cultural group and/or areas of research that need to be expanded or improved and provide an agenda for future research. Describe what area or areas that you think are most important for researchers to focus on and how this may be useful to counselling work with clients from the cultural group. Include at least one (1) recent (last seven years), peer-reviewed source. Write about 200 words for this section. The total number of required recent, peer-reviewed sources is eight (8)) and a maximum of 16 recent, peer-reviewed sources.
Required components: Title page and reference page(s) Length of Assignment: The text body of paper (i.e., not including references and title page; do NOT include an abstract) should consist of approximately 2000 (+/- 100) words, (Times New Roman font size: 12) Format: Please, format your assignment in Word (files with extension .doc or .docx) References: Please provide at least a total of eight (8) recent (last 7 years, currently 2015-2022), peer-reviewed sources and a maximum of 16 recent, peer-reviewed sources. Remember that the course textbooks are not peer-reviewed sources.
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