Minitab Solution Interpretation for the Water/Time Mowing/Temperature example. 

* The printout gives you more information than what is listed below.  We will interpret more of the data later in the rest of the tutorial.*

Regression Analysis

The regression equation is
Water Consumption = - 122 + 12.5 Time mowing + 1.51 Temperature

Step 1 2
Constant -96.85 -121.65
     
Temperature 1.451 1.512
T-Value 7.97 24.89
P-Value 0.001 0.000
     
Time Mow   12.5
T-Value   6.48
P-Value   0.003
     
S 3.78 1.24
R-Sq 92.70 99.37
R-Sq(adj) 91.24 99.05
C-p 43.0 3.0
PRESS 172.265 21.2702
R-Sq(pred) 82.37 97.82

Interpretation of the printout above:  

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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.

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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.
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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.

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R-Sq = 92.7% for step 1 and 99.37% for step 2
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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.

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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.

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Selecting the better model is easy in this case because
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Step 2 is the better model because the R-Sq(pred) value is 97.82%, while the step 1 value is 82.37%.

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S for step2< S for step 1   

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R-sq step 2>R-sq for step 1

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C-p for step 2<C-p for step 1

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R-sq(adj) for step 2>R-sq(adj) for step 1

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The  next step would be a residual analysis on Model 2

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