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LAB 4A: If the Line Fits…

Lab 4A - If the line fits ...

Directions: Follow along with the slides, completing the questions in blue on your computer, and answering the questions in red 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 to improve your predictions?

Predicting heights knowing arm spans

  • Create two subsets of our arm_span data:

    One for armspan >= 61 and armspan <= 63.

    A second for armspan >= 64 and 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.

  • On the Plot pane, click two data points to draw a line through.

  • NOTE: If your line does not appear or it appears but is above the points you selected, zoom out on your browser (typically 50% if you have a Mac, 80% on Windows). Or if your line appears below the points you selected, zoom in on your browser. Then run the add_line() function again and click on two points. Zoom out (or in) until your line appears through the points you selected.

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?