Regression 6. Finding Unknown Parameters with OLS - Solved Manual Example

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You can learn how to perform linear regression by watching my YouTube video.



Numeric Example

A hypothetical dataset about how online gaming habits affects marks involving children in the age group of 10-15 is tabulated. The first feature is the number of hours in a day spent in gaming. The second feature gives the average marks of the students who spend so many hours in gaming.


Problem Statement

Find the regression coefficients m and c in the linear regression model using Least Squares Approach:

y = c+ m*x

Step 1:

We need to check if there is linearity between the dependent and independent variables by plotting the scatter plot.


We see that there is a linear relationship between the data and so we can apply linear regression.

From the blog on OLS, we know to calculate c and m as :

This can be easily calculated by hand with a table as follows:


So, the regression equation representing the relationship between 'Hours Spent' and 'Marks (%)' is:

Marks=89.0−5.5×Hours Spent

This means, for each additional hour spent, the marks decrease by 5.5%, starting from 89% for zero hours spent. ​

Predicting for unseen data

Assume we need to find the marks a student who spends 1.5 hours will get. Plugging in the regression line we get,

Marks = 89 - 5.5*1.5

= 80.75

This helps us predict unseen data with the line of best fit.

Github Link for Code:

ME-CSE-DICS-2019-20/regressionNumericEg-youtube.ipynb at master · lovelynrose/ME-CSE-DICS-2019-20 (github.com)




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