Ontario high school students must complete a minimum of six Ontario Academic Credits (OACs) to gain admission to a university in the province. Most students take more than six OACs because universities take the average of the best six in deciding which students to admit. Most programs at universities require high school students to select certain courses. For example, science programs require two of chemistry, biology and physics. Students applying to engineering must complete at least two mathematics OACs as well as physics. In recent years, one business program began an examination of all aspects of its program, including the criteria used to admit students. Students are required to take English and calculus OACs, and the minimum high school average is about 85%.
Strangely enough, even though students are required to complete English and calculus, the marks in these subjects are not included in the average unless they are in the top six courses in a student's transcript. To examine the issue, the registrar took a random sample of students who recently graduated with the Bachelor of Business Administration degree. He recorded the university GPA (0 to 12), the high school average based on the best six courses and the high school average using English and Calculus and the four next best marks.
Noted:The data for this case; is attached in the Excel filename BQT1614 Assignment Data.
a) Plot the relationship using scatter diagram between the university grades and high school average using the best six OACs. Are the university grades and high school average using the best six OACs linearly related? What can you infer about the relationship between the two variables? Is a linear model appropriate?
b) Compare the scatter plot in (a) with the correlation coefficient. Is it consistent as what you infer from the scatterplot?
c) How much is the extent of the high school average using the best six OACs in influencing the university grades?
d) How much is the variability in the university grades explained by the variability in the high school average using the best six OACs? Explain.
e) Is there any relationship between the university grades and the high school average using the best six OACs? Carry out a test on the significance of the slope.
f) Describe the relationship between the university grades and high school average using English and Calculus and the four next best marks throughthe correlation coefficient.
g) Estimates the least-square regression equation to predict the GPA using high school average using English and Calculus and the four next best marks.
Attachment:- BQT1614-Assignment-Data.rar