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

Interpretation of the printout above:  

• Constant - This is referring to the y-intercept. 

  • -121.655 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. 

  • The slope is equal to 1.51 or approximately 1.5.  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.

• Time mowing - This is also referring to the slope.

  • This slope 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%

  • In our model, the r-sq interpretation is that almost 93% of the variability in the amount of water consumed is explained by the temperature outside.

 

TEMP	Mowed	Water Consumption	TRES1	HI1
75	1.85	16	1.85456	0.670753
83	1.25	20	0.45196	0.454761
85	1.50	25	-0.55759	0.173865
85	1.75	27	-2.73846	0.246620
92	1.15	32	0.10774	0.529086
97	1.75	48	1.19587	0.474723
99	1.60	48	-0.11257	0.450191

• TRES1=This column represents the studentized residuals

  • The studentized residuals are the  standardized residuals with the ith input removed. The fomula is 

   

  

  MSE= mean square error

  

   

   

• Hi1=This column represents the weight of the leverage value (y value) for the ith residual

  • The larger this value is the better fit it becomes until it reaches the value of 2p/n (where p=number of parameters and n=the number of samples) in a large sample size.  When Hi is greater than 2p/n it becomes an outlier and subject to scrutiny.