Part $6$: Test Score

We will now calculate the testing r$-$squared score for our model by repeating the steps from Part $5,$ but using the test set

rather than the training set.

Create a markdown cell with a level $2$ header that reads "Part $6$: Test Score".

In the same cell, add unformatted text explaining that in this section, we will be calculating the test r$-$squared score, and

that we will start by calculating estimated response values for the test set.

Use the variables beta$\_0$ and beta$\_1$ as well as the list x$\_$test to calculate the estimated response values for the test

set. Store the results in a list named pred$\_$y$\_$test. You can accomplish this task using either a loop or a list

comprehension. This cell should not produce any output.

Create a markdown cell explaining that we will now calculate the residuals for the test set.

Use the values stored in y$\_$test and pred$\_$y$\_$test to calculate the residuals for the test set. Store the results in a list

named error$\_$y$\_$test. You can accomplish this task using either a loop or a list comprehension. This cell should not

produce any output.

Before continuing on with our calculation of the r$-$squared score, we will display the true $$ values, the predicted $$ values,

and the residual for each of the first $10$ observations in the test set.

Create a markdown cell explaining that we will be displaying the values mentioned above.

Use a code cell to print the first $10$ values of each of the lists y$\_$test, pred$\_$y$\_$test, and error$\_$y$\_$test. The output

should be formatted in the same way as what was requested for the training set in Part $5.$

Create a markdown cell explaining that we will now calculate the sum of squared errors score for the test set.

Use the values stored in the list error$\_$y$\_$test to calculate the testing sum of squared errors score, storing the result in

a variable name sse$\_$test. Display the result with text output as shown below, rounding the displayed value to $4$

decimal places.

Test SSE $=$ xxxx

Before calculating the test r$-$squared score, we must first calculate the $$ value for the test set. We calculated this for the

training set in Part $3,$ but have not done so for the test set.

Create a markdown cell explaining that we will now calculate the value of $$ on the test set, and will then use that and the

test sum of squared errors to calculate the test r$-$squared score.

Use the formula from Part $3$ to calculate the value $$ for the test set, storing the results in a variable named Syy$\_$test.

Then calculate the test r$-$squared score, storing the result in a variable named r$2\_$test. Display the result with text

output as shown below, rounding the displayed value to $4$ decimal places.

Test r$-$Squared $=$ xxxx

Create a markdown cell explaining that we will now create a plot to visualize the errors for the observations in the test set.

Copy the code below $($without the indentation$)$ into a code cell and then execute that cell.

plt$.$figure$($figsize$=[8,4])$

plt$.$scatter$($x$\_$test, y$\_$test, c$=$'skyblue', edgecolor$=\text{'}$k$\text{'})$

plt$.$plot$([1500,5250],[$beta$\_0+$ beta$\_1*1500,$ beta$\_0+$ beta$\_1*5250],$

c$=$'crimson', lw$=3)$

for i in range$($n$\_$test$)$:

plt$.$plot$([$x$\_$test$[$i$],$ x$\_$test$[$i$]],[$pred$\_$y$\_$test$[$i$],$ y$\_$test$[$i$]],$

c$=$'coral', zorder$=0)$

plt$.$show$()$

Each vertical line shown in this plot represents th