[See Steps] Use the data found in spreadsheet called problem #4 to estimate MCF_t=β_0+β_1*Temp_t+β_2*Weekend_t+β_3*customers_t+β_4*(Temp_t*customers_t)+ε


Question: Use the data found in spreadsheet called problem #4 to estimate

MCFt=β0+β1Tempt+β2Weekendt+β3customerst+β4(Temptcustomerst)+εMC{{F}_{t}}={{\beta }_{0}}+{{\beta }_{1}}*Tem{{p}_{t}}+{{\beta }_{2}}*Weeken{{d}_{t}}+{{\beta }_{3}}*customer{{s}_{t}}+{{\beta }_{4}}*(Tem{{p}_{t}}*customer{{s}_{t}})+\varepsilon

Customers is the number of individual homes in the system. The new variable (Temptcustomerst)(Tem{{p}_{t}}*customer{{s}_{t}}) is called a "cross-product term." We did not study it in class. However, if you truly understand how to answer question 3, you will be able to estimate this equation AND answer the following questions.

  1. What is the marginal impact (onto MCF) if customers increase to 76,000 from 75,000, if it is a weekend and the temperature is 50F 0 ? Does this marginal impact make sense to you? Please explain in a two or three sentences.
    Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
    Intercept 294542.55 58397.57 5.043747 9.96E-07 179412.4 409672.7
    weekend -2445.8883 758.3592 -3.22524 0.001463 -3940.99 -950.792
    temp -4192.0539 946.029 -4.43121 1.52E-05 -6057.14 -2326.97
    customers -2.148916 0.712556 -3.01579 0.002884 -3.55371 -0.74412
    temp*customers 0.034528 0.011521 2.997058 0.003059 0.011815 0.057241

    The fact that we are using a cross product Temp*Costumers means that the effect of a decrease in Costumers depends on the level of variable Temp . In this case, the effect onto MCF is 1000*(-2.148916)+50*1000*0.034528 = -422.516.
    This makes sense, and it takes into account the interaction between the two variables.
  2. What is the marginal impact (onto MCF) if temperature goes DOWN from 50F0 to 49F0 when it is a weekend and there are 75,000 customers? Does this marginal impact make sense to you? Please explain in two or three sentences.

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