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Step-This is referring to which regression equation the
column is explaining
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In the first step we only include temperature as a predictor in
the regression equation, while in the second step we include both temperature
and time mowing in order to see if the extra variable helps create a better
model.
|
|
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Constant - This is referring to the y-intercept.
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In the first step the constant -96.85 is the
amount of water consumption when the temperature is zero. In step
2 the constant -121.65 is the value of water consumption when the
temperature is zero. This means that a person would be expected to
drink about -121.655 ounces of water when the temperature is zero and no
time is spent mowing.
Therefore our model is not applicable around x=0. Our data was
taken in the summer time when the temperatures ranged from 75 to 99
degrees Fahrenheit so our model only predicts for temperatures
approximately in that range. |
|
 |
Temperature - This is referring to the slope.
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In step 1 the slope is equal to1.451. In step 2 the slope is equal to 1.512 .
The slope is equal to (ounces of water)/(degrees F). For our
model, the interpretation of the slope is for each one degree F
increase, you can predict an increase of 1.5 ounces in water
consumption when the Time mowing is held constant or is not included.. |
 |
|
|
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Time mowing - This is also referring to
the slope.
 |
This slope only included in step 2 is equal to 12.53. The slope is equal to
(ounces of water)/(hours spent mowing). For our model, the
interpretation of the slope is for each one hour spent mowing increase,
you can predict an increase of 12.53 ounces in water consumption when
the temperature is held constant. |
|
 | R-Sq = 92.7% for step 1 and 99.37% for step
2
 |
In step 1, the r-sq interpretation is that almost 93%
of the variability in the amount of water consumed is explained by the
temperature outside. In step 2, the r-sq interpretation is that
99.37%
of the variability in the amount of water consumed is explained by the
temperature outside and the amount of time spent mowing. |
|
 | C-p-This
refers to the measure of the differences of the regression model from
the true model. Our goal is for this value to be close to or below
(p+1).
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In step one this value is huge, but in step 2 it
is less than p+1=4 |
|
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PRESS-This
refers to the prediction sum of squares.
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Models with smaller Press values are generally better
models. |
|
 | Selecting the better model is easy in this case because
 | Step 2 is the better model because the R-Sq(pred) value
is 97.82%, while the step 1 value is 82.37%. |
 | S for step2< S for step 1 |
 | R-sq step 2>R-sq for step 1 |
 | C-p for step 2<C-p for step 1 |
 | R-sq(adj) for step 2>R-sq(adj) for step 1 |
|
 | The next step would be a residual analysis on Model
2 |