Qnt. 5040 Mini Report Regressions: The Prescott College General Biology Regression Case | Solution

Qnt. 5040 – Mini Report
Regressions: The Prescott College General Biology Regression Case Study, 2015
Maximum Points: 10
Excel File Needed: Prescott College General Biology Regression Data 2015

Introduction to the Case Study

Nan McPherson, an assistant professor of biology at Prescott College (PC), has been wondering if she could predict the scores on the final exam for her students in a General Biology Class (Bio. 457) and then also predict the student’s final course grade.  She has recorded the exam and final grades for 25 students who took her General Biology class last semester and wants your help in predicting the final exam scores and the final grades for 5 “typical” PC students.

The “typical” PC students are as follows:

Table 1.  Typical General Biology Students at PC

Student’s Name    
Exam 1

(Max. 100 pts.)    
Exam 2

(Max. 100 pts.)    
Exam 3

(Max. 100 pts.)    Predicted Final Exam Score
(Max. 200 pts.)    Predicted Total Course Points
(Max. 500 pts.)    Predicted Course Final Grade
(A to F)
Mary D.    82    86    90            
Mike A.    89    84    87            
Ginny V.    76    79    83            
Isaac G.    60    70    76            
Stan L.    90    91    99            

The professor knows that there are a maximum of 100 points for each of the three unit exams and a maximum of 200 points for the final exam.  Based on the college’s grading scale, the final grade in this course will be determined by the following total point value ranges.

Table 2.    Prescott College Uniform Grading Scheme for General Biology Classes (Max. of 500 points)

        Total Max. Points: 500

Final Grade    
Percentiles    Minimum points    Maximum points
A    94 to 100    470    500
A-    89 to 93    445    469
B+    85 to 88    425    444
B    82 to 84    410    424
B-    78 to 81    390    409
C+    74 to 77    370    389
C    70 to 73    350    369
C-    66 to 69    330    349
D+    61 to 65    305    329
D    57 to 60    285    304
D-    52 to 56    260    284
F    51 and below    0    259

As an example, if student A earns 75, 87, and 90 points on the three unit exams and an additional 168 points on the final exam, their total points would be 420 points and they would earn a B in the class (their total fell into the range of 410 to 424 or the B range from this table above).

Your Tasks

You will help professor McPherson by doing the following tasks and analyzing the results for each task .

1.    Complete a one variable summary for all 25 students over the three unit exams and the final exam.
a.    What do these statistics tell you about the group of students?  Be specific and look at the range, standard deviation, the IQR, the mean versus the median and other statistics from this output.
2.    Complete a single histogram on all four of these test scored and analyze the results.
a.    What do these histograms tell you about the overall grades for each of these exams?
3.    Complete 4 Q-Q plots for these exams.
a.    What do these plots tell you about the data?  Is it relatively normal or not and why?
4.    Complete a single box and whisker plot with all four of the exams on it.
a.    First explain what a box and whisker plot is, and how to understand it.  
b.    What do these box and whisker plots tell you about the individual exams and how do they compare to each other?
5.    Complete a multiple regression using the final exam as the dependent variable, and the unit exams as the independent variables.
a.    Do any of the variables exceed the alpha for this test?  If so, remove that/those variables and rerun the regression.
b.    What does the r-squared value tell you about this data?
c.    What does the standard error of the estimate tell you about the data?
d.    According to the f-ratio, is this regression significant or not and why?
e.    Using the coefficients generate predict the final exam points, the final course total points and the final grade for the five “typical” students found in Table 1 above.  (You are to complete the three columns found on the right in yellow and include this table in your mini report.)
6.    What general things can you tell professor McPherson about the types of students who will either earn a good grades (B to A) or a poor grades (F to D) based on the first three unit exams?  Be specific.  (Yes, you should be able to figure this out, look at the results for both the original data and for the 5 students, that will tell you how to determine who might make good or poor grades.)

Remember to develop your mini report as shown in the chats for this assignment.  All work is to be 1 & ½ spaces, ¾ inch margins, with all tables, graphs and figures having a number and a title and explain in the report.  Include an embedded Excel file showing your work, but note this file will not be graded and is only used to demonstrate that you did the actual work for this case study.

# # #