Multiple regression including categorical independent (dummy variables. The foll

Question

Multiple regression including categorical independent (dummy variables. The following data represent the observed repair times for WaterSoftener Inc.'s machinery. The type of repair is a categorical independent variable. Set mechanical=0, electrical=1. a. Write out the estimated multiple regression equations for both mechanical and electrical softeners. b. What are the estimated repair times for each type of system when It's been five months since the last service? c. Interpret the "months since last service" slope coefficient for your estimated equation.

Explanation / Answer

First i am pasting here regression output here from which can take inferences for solving this quesstion.

a. Estimated Multiple Regression Equation

y = 0.93 + 0.388 * months since last service + 1.2627 * (Type of Machine)

b. If months since last service is 5 months

ThenRepair time for electrical machine = 0.93 + 0.388 * 5 + 1.267 * 1 = 4.137 Hrs

Repair time for mechanical machine = 0.93 + 0.388 * 5 + 1.267 * 0 = 2.87 Hrs

c . The "months since last service" slope coeffcient is 0.388 that means that if there is increase of one month since last service, there is an increase of 0.388 Hrs in repair time.

SUMMARY OUTPUT Regression Statistics Multiple R 0.926928 R Square 0.859195 Adjusted R Square 0.818964 Standard Error 0.459048 Observations 10 ANOVA df SS MS F Significance F Regression 2 9.000923 4.500461 21.357 0.001048 Residual 7 1.475077 0.210725 Total 9 10.476 Coefficients Standard Error t Stat P-value Lower 95% Intercept 0.930495 0.466974 1.992606 0.086558 -0.17372 Months since last service 0.387616 0.062565 6.195396 0.000447 0.239673 Type of Machine 1.262693 0.314127 4.019695 0.005062 0.519902

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