Hello coders, today we are going to solve Day 8: Pearson Correlation Coefficient HackerRank Solution which is a Part of 10 Days of Statistics Series.
Task
The regression line of y on x is 3x + 4y + 8 = 0, and the regression line of x on y is 4x + 3y + 7 = 0. What is the value of the Pearson correlation coefficient?
Solution – Day 8: Pearson Correlation Coefficient
# Step 1, Rewrite the 2 lines in proper form
Rewrite the 2 lines as:
y = -2 + (-3/4) * x
x = -7/4 + (-3/4) * y
so b1 = -3/4 and b2 = -3/4
# Step 2, Apply Pearson's Coefficient formula
Let p = pearson coefficient
Let x_std = standard deviation of x
Let y_std = standard deviation of y
From the tutorial we have:
p = b1 (x_std / y_std)
p = b2 (y_std / x_std)
Multiplying these 2 equations together we get
p^2 = b1 * b2
p^2 = (-3/4) * (-3/4)
p^2 = 9/16
p = 3/4 or -3/4 (depending on correlation of x and y)
# Step 3, Find out if p is postive or negative
Notice that both of the original line equations have negative slopes, so x and y are negatively correlated by definition.
So, p = -3/4
The Correct answer is -3/4.
Disclaimer: The above Problem (Day 8: Pearson Correlation Coefficient) is generated by Hacker Rank but the Solution is Provided by CodingBroz. This tutorial is only for Educational and Learning Purpose.