Exam Questions & Step-by-Step Markschemes (5 Problems)
Question 1 • 2023
5 Marks
For 10 pairs: \sum x = 130, \sum y = 220, \sum x^2 = 2288, \sum y^2 = 5506, \sum xy = 3468 . (i) Find regression equations of y on x and x on y . (ii) Estimate y when x = 16 . (iii) Calculate correlation coefficient r .
Answer: (i) \ y = 1.0167x + 8.783, \; x = 0.9129y - 7.084 \quad (ii) \ y \approx 25.05 \quad (iii) \ r = 0.963
Question 2 • 2024
5 Marks
The two regression equations for variables x and y are 2x + 3y = 6 and 5x + 7y = 12 . (i) Determine which line is the regression line of y on x and which is of x on y . (ii) Find the mean values \bar{x} and \bar{y} . (iii) Calculate the correlation coefficient r .
Answer: (i) \ y\text{ on }x: 2x+3y=6, \; x\text{ on }y: 5x+7y=12 \quad (ii) \ \bar{x} = -6, \bar{y} = 6 \quad (iii) \ r = -\sqrt{14/15} \approx -0.966
Question 3 • 2024
5 Marks
From the following bivariate data, calculate the two regression lines and estimate the value of y when x = 10 : \sum x = 30, \quad \sum y = 40, \quad \sum x^2 = 220, \quad \sum y^2 = 340, \quad \sum xy = 214, \quad n = 5
Answer: y = -0.65x + 11.9; \quad \hat{y}(10) = 5.4
Question 4 • 2023
6 Marks
The two lines of regression are 4x - 5y + 33 = 0 and 20x - 9y - 107 = 0 . Find: (i) The mean values of x and y . (ii) The regression coefficients b_{yx} and b_{xy} . (iii) The coefficient of correlation r between x and y .
Answer: (i) \bar{x} = 13, \, \bar{y} = 17 \quad (ii) b_{yx} = 0.8, \, b_{xy} = 0.45 \quad (iii) r = 0.6
Question 5 • 2024
4 Marks
The equations of two lines of regression are 2x + 3y - 6 = 0 and 5x + 7y - 12 = 0 . (i) Find the mean values of x and y . (ii) Determine which is the regression line of y on x and calculate the correlation coefficient r .
Answer: (i) \bar{x} = -6, \, \bar{y} = 6 (ii) r = -\sqrt{14/15}