Minitab Solution Interpretation for the Water/Temperature/Sun example

The Minitab printout shows the following information.  The interpretation is found below the printout.

The regression equation is

Interpretation of the printout above:  

• For this model, the regression equation is

  Water Consumption = -106.83 + 1.54 Temperature + 5.37 Sun 

  Next, we consider each coefficient in this model seperately.

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

  • -106.83 is the value of water consumption when the temperature is zero.  This means that a person would be expected to drink about -106.83 ounces of water when the temperature is zero and sun is NOT present.  Clearly, our model is not applicable around the temperature of 0 degrees F.  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 for the temperature. 

  • The slope is equal to 1.5385 or approximately 1.5.  The slope is equal to (ounces of water)/(degrees F).  For our model when the sun variable is held constant, the interpretation of the slope is for each one degree F increase, you can predict an increase of 1.5 ounces in water consumption.

• Sun - This is referring to the indicator variable.

  • When sun is present the variable is equal to 1 which pushes the y-intercept up 5.366. When sun is not present the variable is equal to 0, making the corresponding term in the model "disappear."

   

Measuring the fit of the model, Minitab shows:  

S = 2.513 R-Sq = 97.4% R-Sq(adj) = 96.1%

• S = 2.513

  • S is called the Standard Error or the Standard Error of the Estimate.  S is the average squared difference of the error in the actual to the predicted values of the date (i.e. the square root of the mean squared error).  The smaller the value of S, the stronger the linear relationship.

• R-Sq = 97.4%

  • In our model, the r-sq interpretation is that almost 97% of the variability in the amount of water consumed is explained by the temperature outside and the presence or absence of Sun.

• R-Sq(adj) = 96.1%

  • R-squared adjusted is the version of R-squared that has been adjusted for the number of predictors in the model.  R-squared tends to over estimate the strength of the association, especially when more than one independent variable is included in the model.  The R-Sq adjusted is only slightly lower than the R-Sq which indicates that even with the adjustment for adding an extra variable (Sun) we still have a strong association in the model.  

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