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Find the effect of each continuous variable that appears in the model. Let's practice
again with this model using the meadowfoam case study. Our model says that the mean number
of flowers as a function of the light intensity and timing is beta0 plus beta1 times the light
intensity plus beta2 time our early indicator variable. So, the light intensity is the only
continuous variable here, let's find the effect of the light intensity.
So to find the effect light, the first thing we want to do is set down the two means of
interest. So, the definition of an effect is the change in mean response, when the variable
is increased by one. SO you can see I have two means here and I'm comparing them through
subtraction. So, this is the difference of means, or the change in mean response. And
the two means I'm comparing are one in which the light intensity is increased by one and
the early variable is the same. So, you can see here I've got light plus one and light,
so light is one higher on the left hand side here, but early is the same in both cases,
so I'm holding that constant. So, this is the difference in means I need to calculate
the next thing I would do is substitute in the regression model, so on the left hand
side, here, I'm just going to start writing down my regression model and whenever I come
across a light, I'm going to substitute in a light plus one. So, I have beta0 plus beta1
times light, and remember I'm going to put in a light plus one, plus beta2 times early,
we don't have a specific value for early, we are holding it constant. And then we are
going to subtract off the mean on the right hand side, that's a beta0 plus beta1 times
light plus beta2 times early. Ok, now I want to do a little bit of simplification, but
first I'm going to multiply out this term here, so I've got a beta0 plus beta1 times
light, that would be that first term, plus also beta1 times one, which is beta1, plus
beta2 times early. And then there's really nothing to simplify in this second mean, beta0
plus beta1 times light plus beta2 times early. Ok, I'm ready to do the subtraction. There's
always going to be a lot of things that cancel out so there's a beta0 here minus a beta0
here, they'll cancel out. There's a beta1 light and a beta1 light over here, they'll
cancel out. And a beta2 early here and a beta2 early here, they'll cancel out. The only thing
that isn't going to cancel out in this case is this beta1 here. So, the effect of light
in this model, is beta1. If the light intensity is increased by one unit, then we can expect
a change in the mean number of flowers of beta1. In this case because, there is no early
in the result here, the effect of light doesn't depend on the timing. So, I'm just going to
add that, effect of light intensity doesn't depend on timing.