Consider the regression model (8.8) described in Example 8.3 Graph the response function for this model and indicate the role the model parameters play in determining the shape of this function.

Example 8.3

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An electric utility is investigating the effect of the size of a single-family house and the type of air conditioning used in the house on the total electricity consumption during warm-weather months. Let y be the total electricity consumption (in kilo- watt-hours) during the period June through September and x be the size of the house (square feet of floor space). There are four types of air conditioning systems: (1) no air conditioning, (2) window units, (3) heat pump, and (4) central air condi- tioning. The four levels of this factor can be modeled by three indicator variables, X2, X3, and X4, defined as follows: Type of Air Conditioning x2 No air conditioning Window units X3 X4 0 0 0 1 0 0 0 1 0 0 0 1 Heat pump Central air conditioning The regression model is y=Bo+B1x1+B2x2 + B3x3 +4x4 + (8.7)