Technicians at a solar energy company measure heat flux (kilowatts) as part of a
ID: 3357993 • Letter: T
Question
Technicians at a solar energy company measure heat flux (kilowatts) as part of a solar thermal energy test. An energy engineer wants to determine how total heat flux is predicted by other variables: insulation value (watts/meters squared), the position of the east, south, and north focal points (inches), and the time of day. The engineer has asked you for assistance since you are a Six Sigma project manager.
11/8/2017 1:56:32 PM Welcome to Minitab, press Fl for help. Results for: ThermalEnergyTest.MTW Regression Analysis: Heat Flux versus Insulation, East, South, North, Time of Day Analysis of Variance DF Adj SS Adj MS F-Value P-Value 0.000 0.029 0.053 0.016 0.000 0.194 Source 40.84 5.42 18 6.76 72.05 1.79 Regression Insulation East South North Time of Day1 5 13195.5 2639.11 350.6 350.56 270.1 270.13 437.2437.15 1 4656.6 4656.56 115.5 115.50 64.63 1 1 Error Total 23 1486.4 28 14681.9 Model Summary S R-sq R-sa (adj)R-sa (pred 78 . 82% 8.03902 89.88% 8768% Coefficients Term Constant Insulation 0.0675 0.0290 East South North Time of Day Coef SE Coef T-Value P-Value VIF 96.1 0.003 0.029 2.32 0.053 1.36 0.016 3.18 0.000 2.61 0.194 5.37 325.4 2.55 3.80 22.95 2.42 1.25 1.46 2.70 1.81 3.39 2.33 2.04 2.60 8.49 1.34 Regression Equation Heat Flux325.4 0.0675 Insulation 2.55 East 3.80 South- 22.95 North + 2.42 Time of Day Fits and Diagnostics for Unusual Observations Std Fit Resid Resid Obs Heat Flux 271.80 267.574.23 0.97 230.70 213.30 17.40 2.89 R 254.50 240.14 14.36 2.09 R R Large residual X Unusual XExplanation / Answer
Answer:
For the given regression model, the dependent or response variable is given as heat flux while independent variables or explanatory variables are given as insulation, east, south, north, and time of day. From the given Minitab output, the value of the R square or coefficient of determination is given as 89.88%. This means about 89.88% of the variation in the dependent or response variable heat flux is explained by the independent variable or explanatory variables such as insulation, east, south, north, and time of day. The p-value for the coefficient of variable time of the day is given as 0.194 which is greater than the level of significance or alpha value 0.05, so we reject the null hypothesis that the coefficient of variable time of the day is statistically significant. The p-values for another variable east is given as 0.053 which is greater than alpha value 0.05, so coefficient of variable east is statistically significant.
The p-value for overall regression model is given as 0.00, so given regression model is statistically significant.
From the given regression output, the regression equation is given as below:
Heat flux = 325.4 + 0.0675*insulation + 2.55*east + 3.80*south – 22.95*north + 2.42*time of day
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