LAB 4A: If the Line Fits…

Lab 4A - If the line fits ...

Directions: Follow along with the slides and answer the questions in bold 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 LA area, what single height would you choose and why?

    Would you describe this as a good guess? What might you try and 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 an 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 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's. 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.

    – These line connects the mean height of people with similar arm_spans.

    – Fill in the blanks below to create the 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?