# Development of Algae Guard Façade Paint with Statistical Modeling under Natural Phenomena

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

_{c}value) increases by one percent, average algae growth decreases by 12.98%; when temperature increases by 1 °C, average algae growth decreases by 22.4%; a positive unit change in the joint linear effect of dirt resistance, temperature, and humidity caused a decrease in average algae growth by 0.0031%. It was also observed that the individual effect of the humidity variable was inversely related with average algae growth. However, the combination of humidity and temperature, humidity and dirt resistance, humidity and time, and the quadratic effect of humidity were found to increase the average algae growth rate. The cubic effect of temperature variable by one degree centigrade resulted in decrease of average algae growth by 0.000907%.

## 1. Introduction

^{2}-Adj. values, Mallows [38] C

_{p}-values, Root Mean Square Error (RMSE) and Akaike Information Criteria (AIC) [39].

_{c}, Temperature and Humidity.

## 2. Material and Methods

#### 2.1. Chemicals Used

- Reverse Osmosis Treated Water, TDS 0.01, Hardness 4;
- Dispex A-40, Dispersant, solution of an ammonium salt of an acrylic polymer in water, BASF, Ludwigshafen, Germany;
- Magnesium Silicate, 65-micron particle size, Shaheen grinding mills, Lahore, Pakistan;
- Acrysol TT 615, Hydrophobically Modified Anionic Thickener, Rohm and Haas, Philadelphia, PA, USA;
- Zinc Oxide, Bruggemann chemical, Heilbronn, Germany;
- KA-100, Anatase Titanium Dioxide, Kimix, Hangzhou, China;
- TiO
_{2}2310, Rutile Titanium Dioxide, Kronos titanium, Dallas, TX, USA; - Propylene Glycol, Dow, Horgen, Switzerland;
- Wacker 1306, Emulsion of a Polysiloxane Modified with functional Silicone Resin, Wacker, Munich, Germany;
- DisplairCF-245, Mineral Hydrocarbons Defoamer, Whitebirk Ind. Estate, Blackburn, UK;
- AMP-95, 95%, 2-Amino-2-Methyl-1-Propanol Solution, Angus Chemie, GmbH, Ibbenbüren, Germany;
- PST-50A, Styrene Acrylic Copolymer Emulsion, Organic Kimya, Istanbul, Turkey.

#### 2.2. Preparation of Paint Sample

_{c}) indicates the tendency of a surface to resist the accumulation of dirt and average dirt resistance. It is calculated by using standard ASTM D 3719–00 [41]. Algae growth percentage is measured using the software ImageJ 1.50 i “Wayne Rasband, National Institute of Health USA”.

#### 2.3. Experimental Observations

_{c}readings and percentage surface area covered by algae was measured for every slab on the dates mentioned in Table 3. D

_{c}readings were taken using ASTM D 3719–00 [41].

_{c}readings, Initial Lightness (L*a) readings are taken through color Spectrophotometer (BYK Gardner Spectro-Guide Sphere model 6834, BYK-Gardner GmbH, Geretsried, Germany). Final Lightness (L*b) values are taken, on dates mentioned in Table 3, using color Spectrophotometer. Dirt collection index (D

_{c}) is measured according to following formula.

_{c}= (L*b/L*a) × 100

_{c}= Dirt collection index, L*a = Lightness reading of fresh panel, L*b = Lightness reading of dirt exposed panel.

#### 2.3.1. Anderson Darling’s test for Normality

#### 2.3.2. The Coefficient of Determination

^{2}) is used for to explore the variation in the model explained by the independent variables. It is defined as

^{2}value must be large (as close to 1 as possible) [43].

#### 2.3.3. The Adjusted R-square (R^{2}-Adj)

^{2}-Adjis used for judging the goodness of fit and to compare models having different numbers of predictor variables. It is defined as R

^{2}-Adj $=1-\frac{\frac{\mathrm{SSE}}{\left(n-p-1\right)}}{\frac{\mathrm{TSS}}{\left(n-1\right)}}$. It is the unbiased estimate of population coefficient of determination. It is preferred over coefficient of determination R

^{2}as it gives the true change in explained variation due to addition of new explanatory variable [43].

#### 2.3.4. Mallows (1973) C_{p}-values

_{p}-values are the estimated values which are acquired from a fitted regression equation depending on a subset of predictors are usually biased. The mean square error of the estimated value is considered instead of the variance to compare the performance of an equation that is to be considered. The following formula is used to compute the standardized total mean squared error of prediction for the observed data,

^{2}is the random errors variance. To estimate J

_{p}, Mallows (1973) used the statistic,

^{2}and which is obtained from the linear model with the full set of q variables. The expected value of C

_{p}, is p under the assumption of no bias in the fitted model containing p terms. Hence, the deviation of C

_{p}, from p can be taken as a measure of bias. The C

_{p}, statistic therefore is a measure of the performance of the predictors transformed in standardized total mean square error of prediction for the observed data values without considering the actual model which is unknown. It includes both the components including bias and the variance. The subsets of predictors that give the minimum values of C

_{p}, are taken as the anticipated subsets [43].

#### 2.3.5. The Standard Error of Regression

#### 2.3.6. Akaike Information Criteria (AIC)

#### 2.3.7. The Model

_{0}+ β

_{1}(NDP) + β

_{2}(CN-1) + β

_{3}(CN-2) + β

_{4}(Dys) + β

_{5}(Hm) + β

_{6}(Tmp) + β

_{7}(Drt) + β

_{8}(Dys

^{2}) + β

_{9}(Hm

^{2}) + β

_{10}(Tmp

^{2}) + β

_{11}(Drt

^{2}) + β

_{12}(Hm*Tmp) + β

_{13}(Hm*Drt) + β

_{14}(Tmp*Drt) + β

_{15}(Dys

^{3}) + β

_{16}(Hm

^{3}) + β

_{17}(Tmp

^{3}) + β

_{18}(Hm

^{2}*Drt) + β

_{19}(NoD*Drt) + β

_{20}(NoD*Hm) + β

_{21}(Dys*Tmp) + β

_{22}(Dys*Hm

^{2}) + β

_{23}(Hm

^{3}) + β

_{24}(Tmp

^{3}) + β

_{18}(Drt

^{3}) + β

_{25}(Dys

^{2}*Hm) + β

_{26}(Dys

^{2}*Tmp) + β

_{27}(Dys

^{2}*Drt) + β

_{28}(Dys

^{2}*Tmp) + β

_{29}(Dys

^{2}*Drt) + β

_{30}(Dys*Hm*Tmp) + β

_{31}(Dys*Hm*Drt) + β

_{32}(Dys*Tmp*Drt) + β

_{33}(Dys*Drt

^{2}) + β

_{34}(Hm

^{2}*Tmp) + β

_{35}(Hm

^{2}*Drt) + β

_{36}(Hm*Tmp

^{2}) + β

_{37}(Hm*Tmp*Drt) + β

_{38}(Hm*Drt

^{2}) + β

_{39}(Tmp

^{2}*Drt) + β

_{40}(Tmp*Drt

^{2}) + ϵ

_{c}; Dys = Number of days; Tmp = Temperature, °C; Hm = Humidity, %; NDP = 1, Dummy variable for Newly developed paint, = 0, other paint; CN-1 = 1, Dummy variable for conventional Paint A, = 0, other paint; CN-2 = 1, Dummy variable for Conventional Paint B, = 0, other paint and ϵ denotes the error term consisting of unexplained variation in the dependent variable, the Algae growth rate.

_{1}, β

_{2}, ⋯, β

_{40}. Each of the given regression coefficients give the average rate of change in Algae growth rate due to a unit value change in the respective variable. β

_{0}denotes the intercept in the model. For each candidate model corresponding to the respective paint type there will be different value of β

_{0}, which represents the average Algae growth rate when the given paint is to be used after eliminating the effects of all other variables.

## 3. Results, Analysis and Discussion

_{p}, Standard error of regression and AIC were used for choosing the best suitable model as shown in Table 7. Minitab was instructed to include dummy variables at each step as the purpose of study was to predict the Average Algae growth rate on the basis of models for each of the competitive paint type. Table 8 gives the ANOVA for the final model and the expressions of fitted regression equations are also given below.

Algae growth = anti log (−2.7997) = 0.002%

#### Tools to Test the Validity of the Model: Assumptions of the Model

## 4. Conclusions

## 5. Future Work

## Author Contributions

## Funding

## Acknowledgment

## Conflicts of Interest

## Acronyms

ROW | Reverse Osmosis Treated Water |

DIS | Dispex A-40, Dispersant, solution of an ammonium salt of an acrylic polymer in water |

MS | Magnesium Silicate |

HAT | Acrysol TT 615, Hydrophobically Modified Anionic Thickener |

ZO | Zinc oxide |

ATD | KA-100, Anatase Titanium Dioxide |

RTD | TiO_{2} 2310, Rutile Titanium Dioxide |

PG | Propylene Glycol |

PMS | Wacker 1306, Emulsion of a Polysiloxane Modified with functional Silicone Resin |

MHD | DisplairCF-245, Mineral Hydrocarbons Defoamer |

AMP | AMP-95, 95%, 2-Amino-2-Methyl-1-Propanol Solution |

SAC | PST-50A, Styrene Acrylic Copolymer Emulsion |

## References

- Morgans, W.M. Outlines of Paint Technology, 3rd ed.; Griffin: London, UK, 1990. [Google Scholar]
- Gaylarde, C.C.; Morton, L.G. Deteriogenic biofilms on buildings and their control. Biofouling
**1999**, 14, 59–74. [Google Scholar] [CrossRef] - Lakna. Difference between Algae and Fungi. Available online: http://pediaa.com/difference-between-algae-and-fungi (accessed on 26 November 2018).
- Barsanti, L.; Gualtieri, P. Algae: Anatomy, Biochemistry, and Biotechnology, 2nd ed.; CRC Press: Boca Raton, FL, USA, 2006. [Google Scholar]
- Leavitt, P.R.; Findlay, D.L.; Hall, R.I.; Smol, J.P. Algal responses to dissolved organic carbon loss and pH decline during whole-lake acidification: Evidence from paleolimnology. Limnol. Oceanogr.
**1999**, 44, 757–773. [Google Scholar] [CrossRef][Green Version] - Pendersen, M.F.; Hensen, P.J. Effects of high pH on the growth and survival of six marine heterotrophic protests. Mar. Ecol. Prog. Ser.
**2003**, 260, 33–41. [Google Scholar] [CrossRef] - Nakajima, M.; Hokoi, S.; Ogura, D.; Iba, C. Relationship between environmental conditions and algal growth on the exterior walls of the ninna-ji temple, Kyoto. Energy Procedia
**2015**, 78, 1329–1334. [Google Scholar] [CrossRef] - Banov, A. Paints and Coatings Handbook for Contractors, Architects, and Builders, 2nd ed.; Structures Publishing Company: Farmington, MI, USA, 1973. [Google Scholar]
- Falconer, I.R. Potential impact on human health of toxic cyanobacteria. Phycologia
**1996**, 35, 6–11. [Google Scholar] [CrossRef] - Chorus, I.; Bartram, J. Toxic Cyanobacteria in Water: A Guide to the Public Health Consequences, Monitoring and Management, 1st ed.; CRC Press: London, UK, 1999. [Google Scholar]
- Yebra, D.M.; Kill, S.; Darn-Johansen, K. Antifouling technology—Past, present and future steps towards efficient and environmentally friendly antifouling coatings. Prog. Org. Coat.
**2004**, 50, 75–104. [Google Scholar] [CrossRef] - Bruno, D.W.; Ellis, A.E. Histopathological effects in Atlantic salmon, Salmo salar L., attributed to the use of tributyltin antifoulant. Aquacullure
**1988**, 72, 15–20. [Google Scholar] [CrossRef] - Lee, H.B.; Lim, L.C.; Cheong, L. Observations on the use of antifouling paint in netcage fish farming in Singapore. Singap. J. Prim. Ind.
**1985**, 13, 1–12. [Google Scholar] - Konstantinou, I.K. Antifouling Paint Biocides; Springer: Heidelberg, Germany, 2006. [Google Scholar]
- Giacomazzi, S.; Cochet, N. Environmental impact of diuron transformation: A review. Chemsophere
**2004**, 56, 1021–1032. [Google Scholar] [CrossRef] [PubMed] - Diuron Mutagenicity Data; US Environmental Protection Agency (USEPA): Washington, DC, USA, 1986.
- Sorensen, S.R.; Albers, C.N.; Aamand, J. Rapid mineralization of the phenylurea herbicide diuron by Variovorax sp. strain SRS16 in pure culture and within a two-member consortium. Appl. Environ. Microbiol.
**2008**, 74, 2332–2340. [Google Scholar] [CrossRef] [PubMed] - Wang, Z.; Wang, Y.; Gong, F.; Zhang, J.; Hong, Q.; Li, S. Biodegradation of carbendazim by a novel actinobacterium Rhodococcusjialingiae djl-6-2. Chemosphere
**2010**, 81, 639–644. [Google Scholar] [CrossRef] [PubMed] - Amanullah, M.; Hari, B.Y. Evaluation of carbamate insecticides as chemotherapeutic agents for cancer. Indian J. Cancer
**2011**, 48, 74–79. [Google Scholar] [CrossRef] [PubMed] - Guthery, E.; Seal, L.A.; Anderson, E.L. Zinc pyrithione in alcohol based products for skin antisepsis: Persistence of antimicrobial effects. Am J. Infect. Control
**2005**, 33, 15–22. [Google Scholar] [CrossRef] [PubMed] - Cooney, J.J. Effects of polyurethane foams on microbial growth in fuel-water systems. Appl. Microbiol.
**1969**, 17, 227–231. [Google Scholar] [PubMed] - Turley, P.A.; Fenn, R.J.; Ritter, J.C. Pyrithiones as antifoulants: Environmental chemistry and preliminary risk assessment. Biofouling
**2000**, 15, 175–182. [Google Scholar] [CrossRef] [PubMed] - Gibson, W.T.; Hardy, W.S.; Groom, M.H. The effect and mode of action of zinc pyrithione on cell growth. II. In vitro studies. Food Chem. Toxicol.
**1985**, 23, 103–110. [Google Scholar] [CrossRef] - Santa, A.M.; Pozuelo, J.M.; López, A.; Sanz, F. Toxicity of potential irritants in mammalian cells in vitro. Ecotoxicol. Environ. Saf.
**1996**, 34, 56–58. [Google Scholar] - Fonseca, A.J.; Pina, F.; Macedo, M.F.; Leal, N.; Romanowska-Deskins, A.; Laiz, L.; Gómez-Bolea, A.; Saiz-Jimeneze, C. Anatase as an alternative application for preventing biodeterioration of mortars: Evaluation and comparison with other biocides. Int. Biodeterior. Biodegrad.
**2010**, 64, 388–396. [Google Scholar] [CrossRef][Green Version] - Markowska-Szczupak, A.; Ulfig, K.; Morawski, A.W. The application of titanium dioxide for deactivation of bio-particulates: An overview. Catal. Today
**2011**, 169, 249–257. [Google Scholar] [CrossRef] - Caballero, L.; Whitehead, K.A.; Allen, N.S.; Verran, J. Photo inactivation of Escherichia coli on acrylic paint formulations using fluorescent light. Dyes Pigm.
**2010**, 86, 56–62. [Google Scholar] [CrossRef] - Moafi, H.F.; Shojaie, A.F.; Zanjanchi, M.A. Semiconductor-assisted self-cleaning polymeric fibers based on zinc oxide nanoparticles. J. Appl. Polym. Sci.
**2011**, 121, 3641–3650. [Google Scholar] [CrossRef] - Peng, Y.; Ji, J.; Zhao, X.; Wan, H.; Chen, D. Preparation of ZnO Nano powder by a novel ultrasound assisted non-hydrolytic sol–gel process and its application in photo-catalytic degradation of C.I. Acid Red 249. Powder Technol.
**2013**, 233, 325–330. [Google Scholar] [CrossRef] - Roach, P.; Shirtcliffe, N.J.; Newton, M.I. Progress in super hydrophobic surface development. Soft Matter
**2008**, 4, 224–240. [Google Scholar] [CrossRef] - Grant, C.; Hunter, C.A.; Flannigan, B.; Bravery, A.F. The moisture requirements of moulds isolated from domestic dwellings. Int. Biodeterior.
**1989**, 25, 259–284. [Google Scholar] [CrossRef] - Ezeonu, I.M.; Noble, J.A.; Simmons, R.B.; Price, D.L.; Crow, S.A.; Ahearn, D.G. Effect of relative humidity on fungal colonization of fiber glass insulation. Appl. Environ. Microbiol.
**1994**, 60, 2149–2151. [Google Scholar] [PubMed] - Viitanen, H. Factors affecting the development of biodeterioration in wooden constructions. Mater. Struct.
**1994**, 27, 483–493. [Google Scholar] [CrossRef] - Chang, J.C.; Foarde, K.K.; Vanosdell, D.W. Growth evaluation of fungi (Penicillium and Aspergillus spp.) on ceiling tiles. Atmos. Environ.
**1995**, 29, 2331–2337. [Google Scholar] [CrossRef] - Chang, J.C.; Foarde, K.K.; VanOsdell, D.W. Assessment of fungal (Penicillium chrysogenum) growth on three HVAC duct materials. Environ. Int.
**1996**, 22, 425–431. [Google Scholar] [CrossRef] - Flannigan, B.; Morey, P.R. Control of Moisture Problems Affecting Biological Indoor Air Quality; International Society of indoor Air Quality and Climate: Ottawa, ON, Canada, 1996. [Google Scholar]
- Foarde, K.K.; VanOsdell, D.W.; Chang, J.C.S. Evaluation of fungal growth on berglass duct materials for various moisture, soil, use, and temperature conditions. Indoor Air
**1996**, 6, 83–92. [Google Scholar] [CrossRef] - Mallows, C.L. Some comments on C
_{P}. Technometrics**1973**, 15, 661–675. [Google Scholar] - Akaike, H. Information theory and an extension of maximum likelihood principle. In Proceedings of the 2nd International Symposium on Information Theory, Tsahkadsor, Armenia, 2–8 September 1971; Petrov, B.N., Caski, F., Eds.; Akadémiai Kiado: Budapest, Hungary, 1973; pp. 267–281. [Google Scholar]
- ASTM D1210–05 Standard Test Method for Fineness of Dispersion of Pigment-Vehicle Systems by Hegman-Type Gage; ASTM International: Bethesda, MD, USA, 2010.
- ASTM D3719-00 Standard Test Method for Quantifying Dirt Collection on Coated Exterior Panels; ASTM International: Bethesda, MD, USA, 2000.
- Rasband, W. ImageJ. U.S. National Institutes of Health. Available online: https://imagej.nih.gov/ij/ (accessed on 26 November 2018).
- Chatterjee, S.; Hadi, A.S. Regression Analysis by Example, 4th ed.; John Wiley & Sons: Hoboken, NJ, USA, 2015. [Google Scholar]
- Mendenhall, W.; Sincich, T. Simple linear regression. In A Second Course in Statistics: Regression Analysis, 7th ed.; Prentice Hall: Boston, MA, USA, 2012; pp. 104–105. [Google Scholar]

**Figure 1.**Painted slabs with (

**a**) conventional Paint A, (

**b**) conventional Paint B, (

**c**) conventional Paint C, (

**d**) newly developed paint.

Serial No. | Ingredients | Quantity (g) |
---|---|---|

1 | ROW | 27.16 |

2 | DIS | 0.84 |

3 | AMP | 0.60 |

4 | MS | 10.00 |

5 | ZO | 5.00 |

6 | ATD | 20.00 |

7 | RTD | 7.00 |

Total | – | 70.60 |

Serial No. | Ingredients | Quantity (g) |
---|---|---|

1 | Nano mill slurry | 70.60 |

2 | SAC | 20.00 |

3 | PG | 6.00 |

4 | PMS | 2.00 |

5 | HAT | 0.84 |

6 | MHD | 0.56 |

Total | – | 100.00 |

Date | Temperature (°C) | Humidity (%) | Newly Developed Paint | Conventional Paint A | Conventional Paint B | Conventional Paint C | ||||
---|---|---|---|---|---|---|---|---|---|---|

D_{c} Value | Algae % | D_{c} Value | Algae % | D_{c} Value | Algae % | D_{c} Value | Algae % | |||

23/05/2016 | 32.54 | 47.22 | 100.8 | 0.00 | 98.6 | 0.06 | 99.3 | 0.21 | 100.6 | 0.08 |

01/06/2016 | 32.96 | 43.33 | 98.7 | 0.05 | 98.7 | 0.75 | 97.7 | 0.46 | 98.1 | 0.58 |

11/06/2016 | 33.09 | 61.78 | 98.3 | 0.37 | 98.2 | 0.19 | 97 | 0.56 | 97.7 | 0.38 |

21/06/2016 | 33.14 | 66.44 | 98.66 | 0.08 | 98.24 | 0.68 | 96.48 | 0.04 | 97.7 | 0.54 |

01/07/2016 | 32.16 | 76.22 | 98.03 | 0.01 | 97.72 | 0.11 | 96.43 | 0.03 | 97.61 | 0.05 |

11/07/2016 | 30.47 | 79.22 | 98.14 | 0.18 | 98.04 | 0.25 | 96.35 | 0.35 | 97.31 | 0.71 |

21/07/2016 | 29.44 | 80.6 | 97.85 | 0.17 | 97.31 | 0.93 | 96.49 | 0.20 | 97.03 | 0.28 |

01/08/2016 | 29.87 | 78 | 97.91 | 0.03 | 97.47 | 0.04 | 96.11 | 1.39 | 97.08 | 0.05 |

11/08/2016 | 29.78 | 74 | 98.05 | 0.10 | 97.63 | 0.07 | 96.21 | 0.50 | 96.93 | 0.12 |

21/08/2016 | 30.64 | 84.5 | 97.83 | 4.22 | 97.68 | 1.27 | 96.1 | 0.95 | 96.6 | 2.60 |

01/09/2016 | 29.79 | 69.25 | 96.88 | 5.17 | 96.8 | 9.55 | 95.64 | 13.19 | 96.33 | 7.08 |

10/09/2016 | 30.93 | 70.3 | 96.62 | 0.41 | 96.55 | 0.48 | 95.46 | 0.52 | 96.2 | 1.28 |

21/09/2016 | 31 | 75 | 96.99 | 0.15 | 96.96 | 0.36 | 95.43 | 0.16 | 96.35 | 1.62 |

01/10/2016 | 28.07 | 70.44 | 96.16 | 0.17 | 96.09 | 0.61 | 94.3 | 0.93 | 95.62 | 0.45 |

11/10/2016 | 29.59 | 70.44 | 96.1 | 2.40 | 96 | 3.53 | 94.48 | 3.15 | 95.42 | 6.73 |

21/10/2016 | 25.61 | 76.2 | 96.49 | 1.12 | 96.38 | 2.02 | 94.36 | 1.62 | 95.49 | 0.51 |

01/11/2016 | 23.09 | 81.22 | 94.61 | 0.45 | 93.55 | 1.95 | 92 | 0.89 | 91.63 | 0.50 |

11/11/2016 | 20.44 | 73.56 | 95.85 | 0.78 | 95.37 | 2.85 | 93.54 | 6.92 | 94.22 | 1.52 |

21/11/2016 | 19.67 | 72.11 | 94.87 | 1.06 | 94.64 | 3.84 | 93.02 | 8.98 | 93.7 | 2.58 |

01/12/2016 | 18.84 | 86 | 94.08 | 0.85 | 93.97 | 0.74 | 92.92 | 0.45 | 93.84 | 1.68 |

11/12/2016 | 16.92 | 80.78 | 93.96 | 0.20 | 93.86 | 2.81 | 92.79 | 0.22 | 93.77 | 0.21 |

21/12/2016 | 14.6 | 87 | 93.42 | 0.34 | 93.29 | 0.40 | 91.64 | 0.08 | 92.2 | 0.55 |

02/01/2017 | 15.12 | 78 | 93.63 | 0.21 | 93.35 | 0.47 | 91.58 | 0.77 | 92.32 | 0.23 |

11/01/2017 | 14.39 | 84.22 | 93.53 | 0.51 | 93.3 | 0.40 | 91.67 | 0.56 | 92.25 | 0.43 |

21/01/2017 | 11.46 | 80.21 | 93.46 | 1.53 | 93.13 | 0.39 | 92.28 | 1.81 | 93.04 | 1.34 |

21/02/2017 | 16.47 | 62.38 | 93 | 0.70 | 92.95 | 0.87 | 91.27 | 9.96 | 91.94 | 0.77 |

01/03/2017 | 19.21 | 71.7 | 94.37 | 0.32 | 94.17 | 0.32 | 92.21 | 1.55 | 92.38 | 0.98 |

11/03/2017 | 18.53 | 58.65 | 94.31 | 0.60 | 94.23 | 2.86 | 91.94 | 0.71 | 92.11 | 0.40 |

11/04/2017 | 24.68 | 47.22 | 91.71 | 1.32 | 90.96 | 1.53 | 90.49 | 1.87 | 90.07 | 1.84 |

Mean | Standard Deviation | Anderson Darling Statistic Value | p-Value |
---|---|---|---|

1.37 | 2.207 | 16.073 | <0.005 |

Mean | Standard Deviation | Anderson Darling Statistic Value | p-Value |
---|---|---|---|

−0.27 | 0.6928 | 1.0838 | 0.01 |

Regression Variables | Step 15 | Step 16 | Step 17 | |||
---|---|---|---|---|---|---|

Coefficients | p-Value | Coefficients | p-Value | Coefficients | p-Value | |

Constant | 1203 | – | 1234 | – | 1603 | – |

NDP | −0.526 | 0.001 | −0.53 | 0.001 | −0.529 | 0.001 |

CN-1 | −0.157 | 0.282 | −0.159 | 0.271 | −0.159 | 0.269 |

CN-2 | 0.179 | 0.228 | 0.178 | 0.227 | 0.186 | 0.205 |

Dys | 0.053 | 0.788 | −0.003 | 0.981 | −0.004 | 0.966 |

Hm | −27.53 | 0.001 | −27.04 | 0.001 | −34.39 | 0.001 |

Tmp | −20.7 | 0.047 | −22.4 | 0.014 | −31.4 | 0.005 |

Dys*Hm | −0.00338 | 0.232 | −0.00369 | 0.166 | −0.00435 | 0.107 |

Dys*Tmp | 0.00257 | 0.035 | 0.00277 | 0.009 | 0.00436 | 0.005 |

Hm*Tmp | 0.22 | 0.079 | 0.232 | 0.054 | 0.353 | 0.017 |

Dys*Hm*Tmp | – | – | – | – | – | – |

Tmp*Tmp | 0.0787 | 0.004 | 0.0814 | 0.002 | 0.0864 | 0.001 |

DRT | −12.67 | 0.002 | −12.98 | 0.001 | −16.37 | 0 |

Tmp*Drt | 0.205 | 0.047 | 0.2214 | 0.014 | 0.3 | 0.005 |

Tmp*Tmp*DRT | – | – | – | – | – | – |

Hm*DRT | 0.3074 | 0 | 0.3025 | 0 | 0.3712 | 0 |

Hm*Hm | 0.1455 | 0.004 | 0.1386 | 0.002 | 0.1729 | 0.001 |

Dys*Hm*Hm | 0.000033 | 0.123 | 0.000036 | 0.074 | 0.000034 | 0.092 |

Hm*Hm*Tmp | 0.000596 | 0.007 | 0.000592 | 0.007 | 0.000492 | 0.032 |

Hm*Hm*DRT | −0.001708 | 0.001 | −0.001639 | 0 | −0.001948 | 0 |

Tmp*Tmp*Tmp | −0.000866 | 0.036 | −0.000907 | 0.021 | −0.000844 | 0.032 |

Dys*Dys | 0.000047 | 0.417 | 0.000061 | 0.115 | −0.000157 | 0.317 |

Dys*DRT | −0.00058 | 0.741 | – | – | – | – |

Dys*Dys*DRT | – | – | – | – | – | – |

Hm*Tmp*DRT | −0.00299 | 0.016 | −0.0031 | 0.009 | −0.00416 | 0.003 |

Dys*Dys*Hm | – | – | – | – | 0.000004 | 0.154 |

Model Selection Criteria | Step 15 | Statistics | Step 16 | Step 17 |
---|---|---|---|---|

Standard Error | 0.491774 | – | 0.489465 | 0.486741 |

R-sq | 58.81% | 58.77% | 59.65% | |

R-sq(adj) | 49.61% | 50.09% | 50.64% | |

R-sq(pred) | 31.55% | 32.80% | 32.83% | |

Mallows’C_{p} | 23.21 | 21.32 | 21.27 |

Source | Degree of Freedom | Seq SS | Contribution | Adj SS | Adj MS F | p-Value | Value |
---|---|---|---|---|---|---|---|

Regression | 21 | 32.9269 | 59.65% | 32.9269 | 1.56795 | 6.62 | 0 |

Dys | 1 | 8.7024 | 15.77% | 0.0004 | 0.00043 | 0 | 0.966 |

Hm | 1 | 1.5116 | 2.74% | 3.0528 | 3.05282 | 12.89 | 0.001 |

Tmp | 1 | 2.7377 | 4.96% | 1.9725 | 1.97249 | 8.33 | 0.005 |

DRT | 1 | 1.3884 | 2.52% | 3.0968 | 3.09679 | 13.07 | 0 |

NDP | 1 | 1.9468 | 3.53% | 2.7067 | 2.70665 | 11.42 | 0.001 |

CN-1 | 1 | 0.0368 | 0.07% | 0.2928 | 0.29277 | 1.24 | 0.269 |

CN-2 | 1 | 0.0162 | 0.03% | 0.3854 | 0.38536 | 1.63 | 0.205 |

Dys*Dys | 1 | 3.2059 | 5.81% | 0.2393 | 0.23929 | 1.01 | 0.317 |

Hm*Hm | 1 | 0.1791 | 0.32% | 2.8798 | 2.87981 | 12.16 | 0.001 |

Tmp*Tmp | 1 | 0.001 | 0.00% | 2.6893 | 2.68929 | 11.35 | 0.001 |

Dys*Hm | 1 | 0.059 | 0.11% | 0.6287 | 0.62871 | 2.65 | 0.107 |

Dys*Tmp | 1 | 0.0243 | 0.04% | 1.9548 | 1.95478 | 8.25 | 0.005 |

Hm*Tmp | 1 | 0.1876 | 0.34% | 1.3982 | 1.39818 | 5.9 | 0.017 |

Hm*DRT | 1 | 5.0513 | 9.15% | 3.6732 | 3.67321 | 15.5 | 0 |

Tmp*DRT | 1 | 0.0538 | 0.10% | 1.987 | 1.98701 | 8.39 | 0.005 |

Tmp*Tmp*Tmp | 1 | 0.0005 | 0.00% | 1.12 | 1.12393 | 4.74 | 0.032 |

Dys*Dys*Hm | 1 | 0.0861 | 0.16% | 0.4896 | 0.48958 | 2.07 | 0.154 |

Dys*Hm*Hm | 1 | 1.5526 | 2.81% | 0.6873 | 0.68735 | 2.9 | 0.092 |

Hm*Hm*Tmp | 1 | 2.2998 | 4.17% | 1.1293 | 1.12934 | 4.77 | 0.032 |

Hm*Hm*DRT | 1 | 1.7178 | 3.11% | 3.8722 | 3.87216 | 16.34 | 0 |

Hm*Tmp*DRT | 1 | 2.168 | 3.93% | 2.168 | 2.16796 | 9.15 | 0.003 |

Error | 94 | 22.2701 | 40.35% | 22.2701 | 0.23692 | – | – |

Total | 115 | 55.1971 | 100.00% | – | – | – | – |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Qureshi, S.A.; Shafeeq, A.; Ijaz, A.; Butt, M.M. Development of Algae Guard Façade Paint with Statistical Modeling under Natural Phenomena. *Coatings* **2018**, *8*, 440.
https://doi.org/10.3390/coatings8120440

**AMA Style**

Qureshi SA, Shafeeq A, Ijaz A, Butt MM. Development of Algae Guard Façade Paint with Statistical Modeling under Natural Phenomena. *Coatings*. 2018; 8(12):440.
https://doi.org/10.3390/coatings8120440

**Chicago/Turabian Style**

Qureshi, Sheraz Ahmed, Amir Shafeeq, Aamir Ijaz, and Muhammad Moeen Butt. 2018. "Development of Algae Guard Façade Paint with Statistical Modeling under Natural Phenomena" *Coatings* 8, no. 12: 440.
https://doi.org/10.3390/coatings8120440