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Predicting Board Exam Rating from English and Math Grades using Multiple Regression, Quizzes of Statistics

Ateneo de Manila University (ADMU)Statistics

The steps to derive a multiple regression equation for predicting board examination rating based on english and math grades. Correlation coefficients, beta weights, standard deviations, slope calculations, mean values, and the final multiple regression equation. The example uses given data to predict the board examination rating when english grade is 85 and math grade is 75.

Typology: Quizzes

2020/2021

Uploaded on 12/12/2021

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ASSIGNMENT 14
MULTIPLE REGRESSION ANALYSIS
PROBLEM: Below is a table of the grades of a sample of students in English and Mathematics and their
performance in in the board examination.
Let X1 (Y) = Board Examination Performance
X2 = English Grade
X3 = Math Grade
X2 X3 X1 (Y)
85 76 75
77 75 70
92 84 81
80 77 76
75 75 75
88 82 78
96 90 82
83 80 75
87 85 80
90 84 78
Required: Derive a multiple regression equation for predicting board examination rating from
math grade and English grade. Predict board exam rating if X2 = 85 and X3= 75.
1. Correlation Coefficients
a. Correlation between English Grade (X2) and Board Exam Performance (Y)= .852 = .85
b. Correlation between Math Grade (X3) and Board Exam Performance (Y)= .883= .88
c. Correlation between English Grade (X2) and Math Grade (X3) = .913 = .91
2. Beta (β) weights or the Standardized Partial Regression Coefficient
a. Beta weight of the 1st Predictor (English Grade)
β1=(r¿¿x1y)−(r¿¿x2y)(rx1x2)
1−rx1x2
2=¿¿ ¿
(
0.85
)
−(0.88 )(0.91)
1−¿¿
0.286
b. Beta weight of the 2nd Predictor (Math Grade)
β2=(r¿¿x2y)−(r¿¿x1y)(rx1x2)
1−rx1x2
2=0.88−(0.85 )(0.91)
1−¿¿ ¿ ¿
0.6195 = 0.620
pf2

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ASSIGNMENT 14

MULTIPLE REGRESSION ANALYSIS

PROBLEM: Below is a table of the grades of a sample of students in English and Mathematics and their performance in in the board examination. Let X1 (Y) = Board Examination Performance X2 = English Grade X3 = Math Grade X2 X3 X1 (Y) 85 76 75 77 75 70 92 84 81 80 77 76 75 75 75 88 82 78 96 90 82 83 80 75 87 85 80 90 84 78 Required: Derive a multiple regression equation for predicting board examination rating from math grade and English grade. Predict board exam rating if X2 = 85 and X3= 75.

  1. Correlation Coefficients a. Correlation between English Grade (X2) and Board Exam Performance (Y)=. 852 =. b. Correlation between Math Grade (X3) and Board Exam Performance (Y)= .883=. c. Correlation between English Grade (X2) and Math Grade (X3) = .913 =.
  2. Beta (β) weights or the Standardized Partial Regression Coefficient a. Beta weight of the 1st^ Predictor (English Grade)

β 1 =( r ¿¿ x 1 y )−

( r ¿¿ x 2 y )( r x 1 x 2 )

1 − r x^2 1 x 2

b. Beta weight of the 2nd^ Predictor (Math Grade)

β 2 =( r ¿¿ x 2 y )−

( r ¿¿ x 1 y )( r x 1 x 2 )

1 − r x 1 x 2

2 =^

  1. Standard Deviations a. Standard Deviation of X2 (English Grade) = 6. b. Standard Deviation of X3 (Math Grade) = 5. c. Standard Deviation of Y (Board Exam Performance) = **3.
  2. Solve for the slopes or raw score beta weights (b)** a. Slope of the 1st^ Predictor (X 1 = English Grade) b 1 = β 1 ( sy/sx1) = 0.286 (3.56/6.67) = 0. b. Slope of the 2nd^ Predictor (X 2 = Math Grade) b 2 = β 2 ( sy/sx2) = 0.620 (3.56/5.05) = **0.
  3. Solve the Mean Values** a. Mean of X 2 (English Grade) = 85. b. Mean of X 3 (Math Grade) = 80. c. Mean of Y (Board Exam Performance) = 77.
  4. Solve the Y-intercept ( a)

a = Y – b 1 X 1 – b 2 X 2 = 77.00 – 0.153 (85.30) – 0.437 (80.80) = 28.6395 = 28.

7. Derive the Multiple Regression Equation Model : Y = a + b 1 X 1 + b 2 X 2 = Y = 28.64 + 0.153X 2 + 0.437X 3

  1. Predict Y if X 2 = 85 and X 3 = 75 Y = 28.64 + 0.153 (85) + 0.437 (75) = 28.64 + 13.005+ 32.775 = 74. Based on the derived multiple regression equation, if the students’ English grade is 85 and its Math grade is 75 then the predicted rating in the board examination is 74.42.