:5-21 A college student has just completed her junior year. The following table

Question

:5-21 A college student has just completed her junior year. The following table summarizes her grade-point average (GPA) for each of the past nine quarters: GPA 2.4 2.9 3.1 3.2 Year Semester Freshman Fall Winter Spring Fall Winter Spring Fall Winter Spring Sophomore 3.0 2.9 2.8 3.6 Junior 3.2 a. Forecast the student's GPA for the fall semester of her senior year by using a three-period moving average. b. Forecast the student's GPA for the fall semester of her senior year by using exponential smoothing with = 0.2. c. Which of the two methods provides a more accurate

Explanation / Answer

Given, data on the GPA of a college student for the past 9 quarters. The data are as given below.

(a) The three-period moving average from Spring quarter in the Freshman year (q3) to the Spring quarter in the Junior year (q9) is given by:
q3 = (2.4 + 2.9 + 3.1)/3 = 2.8
q4 = (2.9 + 3.1 + 3.2)/3 = 3.1
q5 = (3.1 + 3.2 + 3)/3 = 3.1
q6 = (3.2 + 3 + 2.9)/3 = 3.0
q7 = (3 + 2.9 + 2.8)/3 = 2.9
q8 = (2.9 + 2.8 + 3.6)/3 = 3.1
q9 = (2.8 + 3.6 + 3.2)/3 = 3.2

The forecast for quarter 10 (Fall quarter of Senior Year) is just the moving average for the quarter before that, i.e. the moving average for quarter 9 (Spring quarter of Junior Year) = q9 = 3.2.

(b) Applying exponential smoothing with a smoothing constant of 0.2 we get:

Q1 = Y1 = 2.4
Q2 = 0.2Y2 + 0.8Q1 = 0.2(2.9) + 0.8(2.4) = 2.5
Q3 = 0.2Y3 + 0.8Q2 = 0.2(3.1) + 0.8(2.5) = 2.62
Q4 = 0.2Y4 + 0.8Q3 = 0.2(3.2) + 0.8(2.62) = 2.736
Q5 = 0.2Y5 + 0.8Q4 = 0.2(3) + 0.8(2.736) = 2.7888
Q6 = 0.2Y6 + 0.8Q5 = 0.2(2.9) + 0.8(2.7888) = 2.81104
Q7 = 0.2Y7 + 0.8Q6 = 0.2(2.8) + 0.8(2.81104) = 2.808832
Q8 = 0.2Y8 + 0.8Q7 = 0.2(3.6) + 0.8(2.808832) = 2.967066
Q9 = 0.2Y9 + 0.8Q8 = 0.2(3.2) + 0.8(2.967066) = 3.013653

As before, the forecast for quarter 10 (Fall quarter of Senior Year) is just the value for quarter 9 (Spring quarter of Junior Year) = Q9 = 3.013653 = 3.0 (since GPA is restricted to 1 place of decimal).

Year Freshman Freshman Freshman Sophomore Sophomore Sophomore Junior Junior Junior Quarter Fall Winter Spring Fall Winter Spring Fall Winter Spring GPA 2.4 2.9 3.1 3.2 3 2.9 2.8 3.6 3.2

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