Page 248 - Touhpad Ai

u Slope of the Regression Line: m represents the slope of the line, indicating how much the dependent variable changes
for a unit change in the independent variable.
u Direction of the Relationship: If m is positive, it indicates a positive relationship, meaning that as X increases, Y also
increases. If m is negative, it indicates a negative relationship, meaning that as X increases, Y decreases.
u Rate of Change: The magnitude of m shows the rate at which the dependent variable changes in response to changes
in the independent variable. For example, a larger value of >>> means a steeper slope and a faster change in y for a
given change in x.
u Strength of the Relationship: A larger absolute value of m suggests a stronger relationship between the variables,
while a smaller absolute value of m suggests a weaker relationship.

Least Squares Method—Finding the Line of Best Fit
The Least Squares Method, also known as the Linear Regression Line, is used to find the best-fitting straight line that
minimises the sum of the squared differences between observed and predicted values.
The Least Squares Method, also known as the Linear Regression Line, is used to find the best-fitting straight line that
minimises the sum of the squared differences between observed and predicted values.
Consider the following example, where marks of 10 students are shown, which they scored after a certain number of
hours of study:

No. of Hours Studied Marks
2 44

9 98
5 80
3 75
7 70
1 63

8 53
6 92
2.5 71
4 65

Assuming No. of Hours Studied as x and Marks as y, let us learn to plot the above data on a Scatterplot using Excel.

120

100

80
Marks (Y) 60

40

20

0
0 1 2 3 4 5 6 7 8 9 10
No. of Hours Studied (X)

246 Touchpad Artificial Intelligence - XI