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

(1) Write and run code using 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.
(2) Write and run code making a plot of the height variable.

– (3) If you had to predict the height of someone in the Los Angeles area, what single height would you choose and why?

– (4) Would you describe this as a good guess? What might you try to improve your predictions?

Predicting heights knowing arm spans

(5) Write and run code creating two subsets of our arm_span data:

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

– A second for armspan >= 64 and armspan <= 66.
(6) Write and run code creating a histogram for the height of people in each subset.
Answer the following based on the data:

– (7) What height would you predict if you knew a person had an armspan around 62 inches?

– (8) What height would you predict if you knew a person had an armspan around 65 inches?

– (9) 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.
(10) Write and run code creating a scatterplot for height and armspan. Then run the following code.
```
add_line()
```
On the Plot pane, click two data points to draw a line through.
NOTE: Watch the following video if you are experiencing difficulties obtaining your line https://youtu.be/pGqXHGhhwJ8
If you are unsuccessful using the add_line() function, refer to the next slide to learn how to use the get_line() function.

get_line()

The get_line() function does not rely on clicking on the scatterplot to choose points, but rather on you providing the points manually.
For example, let's say you want to obtain the equation of the line that passes through the points (59,60) and (68,67). This is how you would use the get_line() function:
```
get_line(c(59,60), c(68,67))

##      intercept       slope
##     14.1111111   0.7777778
```
Notice the output is the y-intercept and the slope of your line.
Now you can use the add_line() function to include the line in your scatterplot.
```
add_line(intercept = 14.1111111, slope = 0.7777778)
```
If your line doesn't quite fit the way you want it, try another ordered pair or make modifications to the existing equation.

Predicting with lines

(11) Draw a line that you think is a good fit and write down its equation.
(12) Using your 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.

– (13) How tall would you predict a person with a 63.5-inch armspan to be?

– (14) 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?