As the predicted weight is equal to 197.96 + 0.72

times the volume of the book- 184.05 times cover : pb.

And remember we said that pb, the paperbacks, are the non-reference level.

Meaning that the hardcover books are the reference level.

And for reference levels, we always plug in as 0 in our linear model.

So for hardcover books, if we wanted to simplify this

linear model to see what would it look like only for hardcover books.

We would simply write out our linear model except plug in a 0 for

the cover variable because if you had the reference level, that's a 0.

If you have a book that is a paperback, we would actually plug in 1 for that.

A little bit of simplification gives us that the estimated weight for

hardcover books is 197.96 + 0.72 times the volume.

So here we have started with a multiple regression model and we have simplified

it down to a simple regression model for only one type of the books.

We are able to do this simplification easily because we have a categorical

variable as our second variable in our regression model.

For paperback books on the other hand, we're going to plug in a 1 for

the cover type in our regression model.

So if we simplify that out, we're going to get an intercept of 13.91.

Remember this is a lower intercept than the intercept for the hardcover books,

which makes sense because we had said that paperback books generally weigh

less on average.

So the line for those books should be at a lower spot on the scatter plot

than the line for the hardcover books, plus 0.72 times the volume.

So same slope, different intercepts.

This is what the regression models actually look like on the scatter plot.

For the hardcover books,

we have predicted weight is equal to 197.96 + 0.72 times the volume.

And for paperback books, we have predicted weight = 13.91 + 0.72 times the volume.

What this multiple linear regression has allowed us to do,

is to fit these separate parallel lines for the two types of books.

As opposed to imposing that we pick only one single line,

describing all of these books and imagine that line would be somewhere in between

these two in order to be able minimize the residuals.

But it really wouldn't do a good job explaining either the hardcover or

the paperback books.