FAQ: Linear Regression - Points and Lines

Frequently Asked Questions Python FAQ
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This community-built FAQ covers the “Points and Lines” exercise from the lesson “Linear Regression”.

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This exercise can be found in the following Codecademy content:

Data Science

Machine Learning

FAQs on the exercise Points and Lines

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2 
import codecademylib3_seaborn
import matplotlib.pyplot as plt
months = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
revenue = [52, 74, 79, 95, 115, 110, 129, 126, 147, 146, 156, 184]

In the exercise, what does the first line mean? In order to analyze my own dataset, how to import or apply them in this context?

Thanks,

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I’m not getting passed the first and second exercise on this page. Need a shaming and the solutions please.

https://www.codecademy.com/courses/machine-learning/lessons/linear-regression/exercises/points-and-lines

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How causes changing the values of m and b affect the shape of the line?
image

5

As mentioned in the exercise,

The slope is a measure of how steep the line is, while the intercept is a measure of where the line hits the y-axis.

The equation of a line is

y = mx + b

// m: Slope
// b: y-intercept

In the exercise, we have been provided initial values of m = 8 and b = 40 and have been asked in Step 3 to experiment with these value so that the line matches the revenue data. So, our initial equation of line is:

y = 8x + 40

Look at three situations:

  • Situation 1: Keep m (slope) fixed, but change b (y-intercept)

If you don’t change slope, then the steepness of the line remains unchanged. Changing the y-intercept just moves the line up and down while preserving the steepness. For example,
y = 8x + 60 will shift the line up so that it intercepts the y-axis at a value of 60, but steepness remains unchanged.
y = 8x + 10 will shift the line down so that it intercepts the y-axis at a value of 10, but steepness remains unchanged.
y = 8x - 30 will shift the line down so that it intercepts the y-axis at a value of -30, but steepness remains unchanged.
y = 8x + 0 will shift the line so that it intercepts the y-axis at a value of 0 i.e. it passes through the origin of the axes, but steepness remains unchanged.

  • Situation 2: Change m (slope), but keep b (y-intercept) fixed

If y-intercept is fixed, then we aren’t moving the line up and down. Instead, changing the slope means the steepness of the line is changed. For example,
y = 25x + 40 will intersect the y-axis at a value of 40, but it will rise sharply as we go from left to right along the x-axis (steeper line).
y = 2x + 40 will intersect the y-axis at a value of 40, but it will rise less sharply as we go from left to right along the x-axis (less steeper line).
y = -3x + 40 will intersect the y-axis at a value of 40, but it will slant downwards as we go from left to right along the x-axis.
y = 0x + 40 will intersect the y-axis at a value of 40, and since slope/steepness is 0, so it will be a horizontal line.

  • Situation 3: Change m (slope), and change b (y-intercept)
    This will change both the steepness of the line and the point where y-axis is intersected. Both the shape (steepness) of the line as well as the y-intercept (moving line up and down) are being changed. For Example,
    y = 3x + 15 will intersect the y-axis at a value of 15 and the slope of the line will be 3

In the exercise, you are expected to experiment with values of m and b (i.e. by changing the steepness of the line and moving it up and down) so that the line matches the revenue data.

A visual experiment will be much more instructive than what I wrote. So, I suggest you do the following:

  • Go to an online graphing calculator (https://www.desmos.com/calculator)

  • Enter an equation such as y = 2x + 11 . A line will appear. You can zoom in and out to get a clearer picture.

  • Now experiment with different values of m and b. What happens if you type in y = 2x + 30 or y = 2x - 5 or y = 4x + 11 or y = 16x + 11 or ... ? See how different values of m change the steepness of the line, but doesn’t change the y-intercept. Observe how changing b moves the line up and down, but doesn’t affect steepness. When both m and b are changed, then both changes happen together.

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thanks you very much