Using the regression model, $"$

credit.Im$",$ construct a $95\%$ prediction interval for the credit card balance of a customer when Income$=30,$ Limit$=4500,$ and Student$=$Yes.

predict$($credit$.$lm$,$ data.frame$($Income$=30,$ Limit$=4500,$ Student$=$"Yes"$),$ se$.$fit$=$

Find the standard error of prediction used in the above interval. You can find it in one of the following two ways:

Use the relationship among the three types of standard errors as shown in Slide $14,$ Lecture $9$: $s_p^2=s_f^2+s^2,$ where $s_p$ is the standard error of prediction, $s_f$ is the standard error of fit,

and $s$ is the residual standard error $($which is also given as "residual.scale" in the output$).$

Use the margin of error associated with the interval. The margin of error for the above interval is the multiplication of the critical value $($in this case, qt $(0\mathrm{.}975,396)=1\mathrm{.}966$ and the

standard error of prediction. Round your answer to the nearest integer.

This same question was posted and an expert verification said the answer was $33$ using the second method, but it was not correct when I checked. So perhaps show how to do the first method or both. Thanks!