Regression analysis

Regression analysis

Lessons

Regression analysis is what we call our estimation of our bivariate data
• The simplest model for regression analysis is a “line of best fit” or a “trend line”
Interpolation is our estimation of finding a new data point that lies within our known set of data points.
Extrapolation is our estimation of a new data point that lies outside our known set of data points.
  • Introduction
    What is Regression Analysis?

  • 1.
    Interpolation and Extrapolation
    A study took a sample of 14 cars and found the age of each car and the amount of money that each car is worth. A best fit line is given by the equation y=2100x+27500y=-2100x+27500, where y is the worth of the car in dollars and xx is the age of the car in years.
    Regression analysis and best fit line
    a)
    Using the best fit line interpolate what a car might be worth if it was 5 years old?

    b)
    Using extrapolation what might a car be worth if it was 11 years old?

    c)
    Using extrapolation what might a car be worth if it was 15 years old? What’s wrong with this answer?


  • 2.
    A study was done on 17 factory workers on their coffee consumption and how many boxes they were able to move per hour. The results of this study are given in the graph below:
    Regression analysis and trend line
    The trend line is given as: y=8x+56y=8x+56, with yy being the number of boxes moved per hour and xx being the number of coffees drunk.
    a)
    Using the trend line extrapolate how many boxes would be moved if a worker were to drink 15 coffees?

    b)
    Is the extrapolation done in the previous part a good estimate? Why or why not?


  • 3.
    Finding the Best Fitting Curve
    a)
    Plot the following bivariate data as a scatter plot, with the time spent on homework on the x-axis.

    Time Spent on Homework

    Grade in Class

    2 hours

    65%

    8 hours

    80%

    13 hours

    83%

    15 hours

    87%

    19 hours

    91%

    24 hours

    93%



    b)
    Make a line of best fit using the student who spent 8 hours on homework and the student who spent 15 hours studying

    c)
    Using the best fit line found in the previous part, estimate what mark a student would achieve in this class if they spent 14 hours on homework