LAB 4B: What’s the Score?

Lab 4B - What's the score?

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

In the previous lab, we learned we could make predictions about one variable by utilizing the information of another.
In this lab, we will learn how to measure the accuracy of our predictions.

– This in turn will let us evaluate how well a model performs at making predictions.

– We'll also use this information later to compare different models to find which model makes the best predictions.

Load the arm_span data again.

– Create an xyplot with height on the y-axis and armspan on the x-axis.

– Type add_line() to run the add_line function; you'll be prompted to click twice in the plot window to create a line that you think fits the data well.
Fill in the blanks below to create a function that will make predictions of people's heights based on their armspan:
```
make_predictions <- function(armspans) {
____ * armspans + ____
}
```

Fill in the blanks to include your predictions in the arm_span data.
```
____ <- mutate(____, predictions = ____(____))
```
Now that we've made our predictions, we'll need to figure out a way to decide how accurate our predictions are.

– We'll want to compare our predicted heights to the actual heights.

– At the end, we'll want to come up with a single number summary that describes our model's accuracy.

One method we might consider to measure our model's accuracy is to sum the differences in the actual heights minus our predicted heights.

– What do these differences measure?

– Fill in the blanks below to create a function which calculates the sum of differences:
```
accuracy <- function(actual, predicted) {
sum(____ - ____)
}
```
Then fill in the blanks to calculate our accuracy summary.
```
summarize(____, ____(____, ____))
```

Describe and interpret, in words, what the output of your accuracy summary means.

– Compare your accuracy summary with a neighbors. Whose line was more accurate and why?
Write down why adding positive and negative errors together is problematic for accessing prediction accuracy.

– Why does calculating the squared values for the differences solve this problem?
Alter your accuracy function to first calculate the differences, then square them and finally take the mean of the squared differences. This is called the mean squared error (MSE).

– Calculate the MSE of your line.

Create a regression line as you did in the previous lab, for height and armspan.

– We also refer to regression lines as linear models.

– Assign this model the name best_fit.
Making predictions with models R is familiar with is simpler than with lines, or models, we come up with ourselves.

– Fill in the blanks to make predictions using best_fit:
```
____ <- mutate(____, predictions = predict(____))
```
Calculate the MSE for these new predicted values.

The lm() function creates the line of best fit equation by finding the line that minimizes the mean squared error. Meaning, it's the best fitting line possible.

– Compare the MSE value you calculated using the line you fitted with add_line() to the the same value you calculated using the lm function.

– Ask your neighbors if any of their lines beat the lm line in terms of the MSE. Were any of them successful?
To see how the lm line fits your data, create a scatterplot and then run:
```
add_line(intercept = ____, slope = ____)
```