Question

The following scatter plot shows the number of page views for a popular website and how many people signed up to receive emails from the company for upcoming events.

1) Draw a line of best fit on the scatter plot.
2) Find the slope and y-intercept
3) Write an equation for the line of best fit drawn

Answer 1

See Explanation.

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Equality Properties

• Multiplication Property of Equality
• Division Property of Equality
• Addition Property of Equality
• Subtract Property of Equality

Algebra I

Slope Formula:
`\displaystyle m=(y_2-y_1)/(x_2-x_1)`

Slope-Intercept Form: y = mx + b

• m - slope
• b - y-intercept

Linear Regression

Explanation:

We can draw any best line of fit, as long as it is reasonable around the points that are given.

We can just take 2 points and use slope formula and Slope-Intercept Form to find the equation for the best line of fit.

Using Linear Regression, we can determine the true best line of fit using graphing utilities.

Finding the best line of fit

Define 2 points

Point (21600, 205)

Point (27000, 290)

Find slope m

1. Substitute in point [SF]:
   `\displaystyle m=(290-205)/(27000-21600)`
2. [Fraction] Subtract:
   `\displaystyle m=(85)/(5400)`
3. [Fraction] Simplify:
   `\displaystyle m=(17)/(1080)`

Find equation

1. Define equation [SIF]:
   `\displaystyle y = (17)/(1080)x + b`
2. Substitute in point:
   `\displaystyle 290 = (17)/(1080)(27000) + b`
3. Multiply:
   `\displaystyle 290 = 425 + b`
4. Isolate y-intercept b:
   `\displaystyle -135 = b`
5. Rewrite:
   `\displaystyle b = -135`
6. Redefine equation:
   `\displaystyle y = (17)/(1080)x - 135`

Slope-Intercept Form tells us that our slope m =
`\displaystyle (17)/(1080)` and our y-intercept
`\displaystyle b = -135`.

Setting this as function f(x), we can see from the graph that it is extremely accurate (Blue line).

Using Linear Regression

Depending on the graphing calc you have, the steps may be different.

Using a graphing calc, we can use statistics and determine the best best line of fit.

When we determine the values, we should see that our equation would be g(x) (Green Line).

Credit to Lauren for collabing w/ me in graphing.