Finding the Bootstrap Prediction Interval

predictions about a bird's weight based on the weight of the corresponding egg.

However, just as we're uncertain about the slope of the true regression line, we're also uncertain about the predictions made based on the true regression line.

Question $2\mathrm{.}1.$ Define the function fitted$\_$value $.$ It should take in four arguments:

table: a table like birds. We'll be predicting the values in the second column using the first.

$x_{?}$col : the name of our $x-$column within the input table

$y\_$col : the name of our $y-$column within the input table

given$\_$x : a number, the value of the predictor variable for which we'd like to make a prediction.

The function should return the line's prediction for the given $x.$

Hint: Make sure to use the fit$\_$line function you defined in Question $1\mathrm{.}3.$

Fit line function:

def fit$\_$line$($tbl$,$ x$\_$col, y$\_$col$)$

x $=$ tbl$[$x$\_$col$]$

y $=$ tbl$[$y$\_$col$]$

slope,intercept $=$ np$.$polyfit$($x$,$y$,1)$

return $[$slope$,$ intercept$]$

fit$\_$line $($birds$,$ "Egg Weight" $,$ "Bird Weight"$)$