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.

add_line()

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?