Equation of the best fit line

Equation of the best fit line

Lessons

The best fit line has the equation: y=ax+by=ax+b, where aa and bb are given as:
• a=n∑xy−∑x∑yn∑x2−(∑x)2a=\frac{n\sum xy-\sum x \sum y}{n\sum x^2-(\sum x)^2}
• b=y‾−ax‾b=\overline{y}-a\overline{x}
  • Introduction

    • Formula for the Best Fit Line
    • What are Residuals?
  • 1.
    Determining the Equation for a Best Fit Line
    Given the following bivariate data give the equation for the best fit line and plot it on the given graph.

    x

    y

    1

    2

    2

    2

    3

    4

    4

    5


    Plot the best fit line
  • 2.
    Determining the Equation for a Best Fit Line using Calculator Commands
    For the following bivariate data:

    x

    y

    1

    9

    2

    7

    3

    8

    4

    5

    5

    5

    6

    3

    7

    2


    a)
    Using a graphing calculator plot the points on a graph

    b)
    Still using your graphing calculator find the equation for the best fit line and plot it on the same graph

  • 3.
    Interpretation graphical Data
    In Skyrim (a video game) I plotted what level I was when I killed my first 5 dragons. The graphical data is given below:

    # of dragons killed

    Corresponding level

    1

    Level 4

    2

    Level 5

    3

    Level 6

    4

    Level 6

    5

    Level 7


    Equation of the best fit line
    a)
    What is the sum of all the residuals squared?

    b)
    Using the data above extrapolate what my level will be when I kill my 8th dragon. Is this a good estimation? Why or why not?

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3.
Data Interpretation
3.1
Center of a data set: mean, median, mode
3.2
Spread of a data set - standard deviation & variance
3.3
Measures of relative standing - z-score, quartiles, percentiles
3.4
Bivariate, scatter plots and correlation
3.5
Regression analysis
3.6
Equation of the best fit line
Statistics