Example of Regression Line
Example 1:
A function facilitates the calculation of marks scored by the students when the number of hours studied by them is given. The slope and y-intercept of the given function are 5 and 50 respectively. Using this information, form a regression line equation.
Solution:
In case of calculation of marks scored by students, when the numbers of hours each of them studied are given, Marks will be the dependent variable (i.e. marks will be represented by Y) and number of hours studied will be the dependant variable (i.e. number of hours studied by the students will be represented by X). Now, the general linear regression equation is Y = a + bX.
We have been given that the y-intercept is 50, (i.e., a = 50) and the respective slope is 5, (i.e. b = 5).
Therefore, the required equation of regression line will be,
Y = 50 + 5X + ε
Example 2:
In continuation with the above example, the figures of three students are given as follows:
Student 1: Studied for 2 hours and scored 60 marks.
Student 2: Studied for 3 hours and scored 65 marks.
What will the marks scored by the 4th student in case he/she studies for 5 hours.
Solution:
The required equation of regression line as calculated in previous example is,
Y = 50 + 5X
In case of 4th student, who studies for 5 hours (X = 5), the marks scored by him will be calculated as,
Y = 50 + 5X.
Y = 50 + 5(5)
Y = 75 Marks