If the line fits ...

Lab 4A

Directions: Follow along with the slides and answer the questions in red font in your journal.

How to make predictions

  • Anyone can make predictions.
    • Data scientists use data to inform their predictions by using the information learned from the sample to make predictions for the whole population.
  • In this lab, we'll learn how to make predictions by finding the line of best-fit.
    • You will also learn how to use the information from one variable to make predictions about another variable.

Predicting heights

  • Use the data() function to load the arm_span data.
  • This data comes from a sample of 90 people in the Los Angeles area.
    • The measurements of height and armspan are in inches.
    • A person's armspan is the maximum distance between their fingertips when they spread their arms out wide.
  • Make a plot of the height variable.
    • If you had to predict the height of someone in the Los Angeles area, what single height would you choose and why?
    • Would you describe this as a good guess? What might you try to improve your predictions?

Predicting heights knowing arm spans

  • Create two subsets of our arm_span data:
    • One for armspan >= 61 & armspan <= 63.
    • A second for armspan >= 64 & armspan <= 66.
  • Create a histogram for the height of people in each subset. Answer the following based on the data:
    • What height would you predict if you knew a person had an armspan around 62 inches?
    • What height would you predict if you knew a person had an armspan around 65 inches?
    • Does knowing someone's armspan help you predict their height? Why or why not?

Fitting lines

  • Notice that there is a trend that people with a larger armspan also tend to have a larger mean height.
    • One way of describing this sort of trend is with a line.
  • Data scientists often fit lines to their data to make predictions.
    • What we mean by fit is to come up with a line that's close to as many of the data points as possible.
  • Create a scatterplot for height and armspan. Then run the following code. Draw a line by clicking twice on the Plot pane.

Predicting with lines

  • Draw a line that you think is a good fit and write down its equation. Using this equation:
    • Predict how tall a person with a 62 inch armspan and a person with a 65 inch armspan would be.
  • Using a line to make predictions also lets us make predictions for armspans that aren't in our data.
    • How tall would you predict a person with a 63.5 inch armspan to be?
  • Compare your answers with a neighbor. Did both of you come up with the same equation for a line? If not, can you tell which line fits the data best?

Regression lines

  • If you were to go around your class, each student would have created a different line that they feel fit the data best.
    • Which is a problem because everyone's line will make slightly different predictions.
  • To avoid this variation in predictions, data scientists will use regression lines.
    • This line connects the mean height of people with similar arm_spans.
    • Fill in the blanks below to create a regression line using an lm, or linear model:
lm(____ ~ ____, data = arm_span)

Predicting with regression lines

  • Use the output of the code from the previous slide to write down the equation of the regression line in the form
    y = a + bx.
  • Add this line to a scatterplot by filling in the blanks below:
add_line(intercept = ____, slope = ____)
  • Predict the height of a person with a 63.5 inch armspan and compare it with a neighbor. Ensure you both arrive at the same predicted value.
  • Measure your armspan and use the regression line to predict your height. How close was the prediction?