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\title{Performance Analysis of Mild Steel (ASTM A36) under Varying Drilling Conditions using Taguchi and ANOVA}
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             \author[1]{Tanzila  Lutfor}

             \author[2]{Sohag  Sarker}

             \author[3]{Md. Zahangir  Alam}

             \affil[1]{  Pabna University of Science and Technology}

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\date{\small \em Received: 14 December 2012 Accepted: 4 January 2013 Published: 15 January 2013}

\maketitle


\begin{abstract}
        


In this paper, the performance of a single-inputmultiple- output (SIMO) scheme is analyzed under Rayleigh and Rician fading channel using Maximal-Ratio Combining (MRC) and Equal Gain Combining (EGC). In this scheme, a single transmit antenna, which maximizes the total received signal power at the receiver is used and number of received antenna is varied to analyze performance. The Bit Error rate(BER) using two combining techniques under fading channels is derived for BPSK, QPSK and 16-QAM.

\end{abstract}


\keywords{rayleigh fading, rician fading, maximal-ratio combining, and equal gain combining.}

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\let\tabcellsep& 	 	 		 
\section[{I. Introduction \& Literature Review}]{I. Introduction \& Literature Review}\par
Anderson \& Whitcomb (2016) defined Minimum Quantity Lubrication (MQL) as the use of cutting fluids of only a minute amount-typically of a flow rate of 50-500 ml/hour-which is about three to four orders of magnitude lower than the amount commonly used in flood cooling. The concept of Minimum Quantity Lubrication (MQL), sometimes referred to as near dry lubrication 'or micro lubrication \hyperref[b1]{(Asad, Girardin, Mabrouki \& Rigal, 2008)}.\par
A large amount of heat is generated in dry machining because of rubbing between the cutting tool and workpiece. The application of cutting fluid during machining operation reduces cutting zone temperature and increase tool life yet it causes skin and lung disease to the operators and air pollution \hyperref[b2]{(Ezugwu \& Lai, 1995;}\hyperref[b3]{Beaubien \& Cattaneo, 1964)}.\par
Ahsan, Kibria, Ahmed, Islam \& Hossain (2010) found that MQL generally uses vegetable oil or ester oil as the cutting fluid. These high-performing oils have excellent lubrication and natural dissolving properties. This result avoids pollution of the environment and related problems of health and safety, and drastically reduces lubricant costs \hyperref[b23]{(Khan, Mithu \& Dhar, 2009)}, although it may cause problems of corrosion \hyperref[b24]{(Kirkaldy \& Young, 1987)}. Furthermore, they are environmentally friendly \hyperref[b23]{(Khan, Mithu \& Dhar, 2009)}. In our study, Diod sol-M is used as a lubricant. According to a survey conducted by the European Automobile Industry, the cost incurred on lubricants comprises nearly 20\% of the total manufacturing cost. The cost of the cutting tool is only 7.5\% of the total cost \hyperref[b5]{(Brockhoff \& Walter, 1998)}.\par
Braga, Diniz, Miranda, \& Coppini (2002) compared the performances of the uncoated and diamond coated carbide drills, using minimal lubrication (10 ml/h of oil in a flow of compressed air) and abundant soluble oil as a refrigerant/lubricant in the drilling of aluminum-silicon alloys (A356).\par
In the experiments cutting speeds of 10-50 m/min and feed of 0.1-0.2 mm were used. The lubrication was applied either with an external nozzle or internally through the drill. It was concluded that the measured temperature with the application of MQL internally through the tool was 50\% smaller than those obtained with MQL applied with an external nozzle. When MQL was applied with an external nozzle the greatest temperature was measured in a piece drilled with an uncoated drill. For different coatings, there was no significant variation in temperature \hyperref[b8]{(Zeilmann \& Weingaertner, 2006)}. A study was conducted at Georgia Institute of Technology to compare the mechanical performance of minimum quantity lubrication over J completely dry lubrication for the turning of hardened rilling is the operation of cutting a hole of circular cross-section in solid materials using a drill bit. The drill bit is usually a rotary cutting tool, often multipoint. The drill bit is pressed against the workpiece and rotated at rates from hundreds to thousands of revolutions per minute. A drilling machine comes in many shapes and sizes, from small hand-held power drills to bench mounted and finally floor-mounted models. They can perform operations other than drilling, such as countersinking, counterboring, ream, and tap large or small holes \hyperref[b21]{(Eskicioglu \& Davies, 1983}; Kibbe, White, Meyer, Curran, \& Stenerson, 2014; \hyperref[b20]{Lemelson, 1967)}. 
\section[{D A36)}]{D A36)}\par
Abstract-This study is conducted to analyze the performance of Mild Steel (ASTM A36) using a drill bit (8.25mm \&10.25mm high-speed steel) at two different speeds (270 \& 630 RPM) under the three conditions (Dry, MQL, and Wet). The Taguchi has been introduced to find out the most influential factors and most of the cases it was drilling conditions. This performance study has been accelerated by using minitab18 software for ANOVA analysis. Thus it gives the clear indication about the effects of RPM, drilling conditions and drill bit size on drilling a particular materials MS (ASTM A36). The conditions and factors have been shown whether it is statistically significant and how much. One conspicuous thing that the interaction between conditions and factors also have the significant effect. The wet cooling condition has shown the better performance on surface roughness for all conditions and drill bit size. The drilling under wet cooling and MQL conditions have almost the same results but it varies in the case of the dry condition. Low RPM is found to be statistically significant than it is for high RPM. The regression line equation can bring the remarkable significance of further drilling Mild Steel at any drilling conditions.\par
bearing-grade steel materials with low content CBN cutters \hyperref[b9]{(Liang \& Ronan, 2003)}.\par
A series of MQL drilling tests were conducted to determine if a high penetration rate could be achieved under oil delivery rate was 50 ml/hr, Air pressure for all tests was 4.96 bars, and air consumption was approx. 31 l/min. It was concluded that MQL process costs were approximately 10\% lower than the traditional machining process. Dry chips were produced and could have been sold to a recycling facility without additional processing. Air quality for MQL was better than conventional machining, with a significant reduction in aerosol particle concentration \hyperref[b10]{(Filipovic \& Stephenson, 2006)}. Taguchi method analyzes the influence of parameter variation on response characteristics. Thereby, and an optimal result can be obtained from the sensitivity analysis respect to parameter variation. However, Taguchi method has shown some defects in dealing with the problems of multiple performance characteristics \hyperref[b11]{(Bement, 1989} The lubricating agent needs to be supplied at high pressure and impinged at high speed through the nozzle at the cutting zone under MQL condition. Considering the requirements for the present work and uninterrupted supply of MQL at constant pressure, an MQL delivery system has been designed and fabricated. The thin but high-velocity stream of MQL was projected in such a direction so that the coolant could reach as close to the chip-tool and the work-tool interfaces as possible.   
\section[{III. Data Analysis And Interpretation}]{III. Data Analysis And Interpretation}\par
The data obtained from the experimental investigation are analyzed with two statistical tools Taguchi and ANOVA. All collected data were recorded using Microsoft Excel and transferred to Minitab 17    {\ref 4}.1 shows the effect of cutting condition, cutting speed and their interaction on surface roughness. For speed the null hypothesis is accepted, that is, there is no statistically significant difference in the mean between the different groups of independent variables. But for the condition the null hypothesis is rejected, that is, there is a statistically significant difference in the mean between the different groups of independent variables. The interaction effect is not statistically significant. That is, the effect of cooling condition on surface roughness is not dependent on cutting speed (and vice versa).\par
The surface roughness analysis of variance results for drilling mild steel with 10. \hyperref[b25]{25}    {\ref 4}.2 shows the effect of cutting condition, cutting speed and their interaction on surface roughness. For the speed and conditions the null hypothesis is rejected, that is, there is a statistically significant difference in the mean between the different groups of independent variables. The interaction effect is not statistically significant. That is, the effect of cooling condition on surface roughness is not dependent on cutting speed (and vice versa).\par
V. The performance of MS (ASTM A36) is highlighted in a graphical manner to aid the analysis. The correlation analysis for surface roughness has been shown with respect to the no. of holes drilled under varying drilling conditions. The graphical results support as the results found in both Taguchi and ANOVA. 
\section[{Graphical Analysis}]{Graphical Analysis}\par
From Fig.  {\ref 5}.1 Main effects and Interaction effects plot for S/N Ratio, it has been seen that the in the wet condition the roughness is better than the MQL and dry respectively. Here the drilling conditions are the most influential factors than RPM and Feed. Also, the high feed and low RPM is better for surface roughness. Performance measure on MQL and wet machining have almost the same results.\par
From Fig.  {\ref 5}.2 Main effects and Interaction effects plot for surface roughness, it has been noticed that For 8.25 mm drill bit, Surface roughness varies in the range of 3.034 to 3.962 mm for dry machining. Surface roughness varies in the range of 2.565 to 3.596 mm for MQL machining. Surface roughness varies in the range of 2.458 to 3.47 mm for flood machining. It can be seen from the graph that surface roughness for MQL machining is closer to flood machining than dry machining. For 10.25 mm drill bit, Surface roughness varies in the range of 2.940 to 3.909 um for dry machining. Surface roughness varies in the range of 2.552 to 3.021 mm for MQL machining. Surface roughness varies in the range of 2.425 to 2.898 mm for flood machining. It can be seen from the graph that surface roughness for MQL machining is closer to flood machining than dry machining. 
\section[{VI.}]{VI.} 
\section[{Findings}]{Findings}\par
Taguchi, ANOVA, and graphical analysis results under varying drilling conditions, Drill bit size and RPM are: a) Drilling conditions are the most influential factor b) Wet machining condition is better for surface roughness c) Low rpm (270 rpm) is better for surface roughness d) For 8.25mm drill bit, the speed, conditions, and interaction effect are not statistically significant that is there is no statistically significant difference in the mean between the different groups of independent variables. e) For 10.25mm drill bit, the speed and conditions have statistical significance but interaction effect is not statistically significant. f) Performance measure on MQL and wet machining have almost the same results.\par
VII. 
\section[{Conclusion}]{Conclusion}\par
at varying drilling conditions, drill bit size and RPM is very useful research work in the field of manufacturing. Statistical tools Taguchi, ANOVA are used to analyze the performance of surface roughness under varying conditions and factors. Drilling conditions are found to be most influential factors rather than drill bit size and RPM. Wet machining conditions and low RPM is better for surface roughness. This research work will help to\begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_0}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_1}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-4.png}
\caption{\label{fig_2}Figure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{51}\includegraphics[]{image-5.png}
\caption{\label{fig_3}Fig. 5 . 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{31} \par 
\begin{longtable}{P{0.85\textwidth}}
Year 2018\\
8\\
( ) Volume XVIII Issue III Version I\\
Global Journal of Researches in Engineering\end{longtable} \par
  {\small\itshape [Note: J© 2018 Global Journals statistical software for the ANOVA analysis. Before ANOVA analysis the normality test has been performed to check whether the data is normal \& fit for the ANOVA analysis. A36) under varying drilling conditions.]} 
\caption{\label{tab_0}Table 3 . 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{32} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_1}Table 3 . 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{33} \par 
\begin{longtable}{P{0.04881398252184769\textwidth}P{0.21223470661672908\textwidth}P{0.13264669163545567\textwidth}P{0.02175405742821473\textwidth}P{0.018039950062421973\textwidth}P{0.3809612983770287\textwidth}P{0.01963171036204744\textwidth}P{0.015917602996254682\textwidth}}
\tabcellsep \tabcellsep \multicolumn{3}{l}{S/N response (Drill bit: 8.25mm)}\tabcellsep \multicolumn{3}{l}{Mean response (Drill bit: 8.25mm)}\\
\tabcellsep Level\tabcellsep Condition's (Dry, MQL ,Wet)\tabcellsep RPM (270 \& 630 rpm)\tabcellsep Feed (mm/rev)\tabcellsep Condition's (Dry, MQL ,Wet)\tabcellsep RPM (270 \& 630 rpm)\tabcellsep Feed (mm/rev)\\
\tabcellsep 1\tabcellsep -11.212\tabcellsep -10.095\tabcellsep -9.991\tabcellsep 3.646\tabcellsep 3.230\tabcellsep 3.180\\
\tabcellsep 2\tabcellsep -9.603\tabcellsep -10.170\tabcellsep -10.273\tabcellsep 3.043\tabcellsep 3.247\tabcellsep 3.297\\
\tabcellsep 3\tabcellsep -9.582\tabcellsep \tabcellsep \tabcellsep 3.026\tabcellsep \tabcellsep \\
Year 2018\tabcellsep Delta Rank\tabcellsep 1.630 1\tabcellsep 0.075 3\tabcellsep 0.282 2\tabcellsep 0.62 1\tabcellsep 0.017 3\tabcellsep 0.117 2\\
10\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
J ( ) Volume XVIII Issue III Version I\tabcellsep Level 1 2 3 Delta\tabcellsep \multicolumn{3}{l}{S/N response (Drill bit: 10.25mm) Condition's (Dry, MQL ,Wet) RPM (270 \& 630 rpm) Feed (mm/rev) -10.702 -9.370 -9.991 -9.037 -9.799 -10.273 -9.014 1.688 0.429 2.313}\tabcellsep \multicolumn{3}{l}{Mean response (Drill bit: 10.25mm) Condition's (Dry, MQL ,Wet) RPM (270 \& 630 rpm) Feed (mm/rev) 3.437 2.961 3.022 2.833 3.106 3.044 2.830 0.607 0.145 0.022}\\
Global Journal of Researches in Engineering\tabcellsep \multicolumn{3}{l}{IV. Rank a) ANOVA Assumptions Anova Analysis 2 3}\tabcellsep 1\tabcellsep \multicolumn{3}{l}{1 b) ANOVA Hypothesis 1. Null Hypothesis: There is no significant difference 2 3 between the responses obtained by varying the individual input variables. 2. Alternate Hypothesis: There is a significant difference between the responses obtained by varying the individual input variables. c) ANOVA Results For ease of use, the following factors have been coded as below when used in Minitab. Dry: Coded as 11 MQL: Coded as 12 Wet: Coded as 13}\\
\tabcellsep \multicolumn{4}{l}{1. Individual differences and errors of measurement are normally distributed within each group.}\tabcellsep 270 RPM: Coded as 1 630 RPM: Coded as 2\tabcellsep \tabcellsep \\
\tabcellsep \multicolumn{4}{l}{2. Size of the variance and distribution of individual}\tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \multicolumn{4}{l}{differences and random errors are identical in each}\tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep group.\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \multicolumn{4}{l}{3. Individual differences and errors of measurement}\tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \multicolumn{3}{l}{are independent of the group to group.}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep © 2018 Global Journals\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_2}Table 3 . 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{41} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_3}Table 4 . 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.568232044198895\textwidth}P{0.004025256511444357\textwidth}P{0.06306235201262826\textwidth}P{0.04763220205209155\textwidth}P{0.08251775848460931\textwidth}P{0.016771902131018153\textwidth}P{0.03891081294396211\textwidth}P{0.014088397790055248\textwidth}P{0.014759273875295976\textwidth}}
Table\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\multicolumn{3}{l}{Analysis of Variance}\tabcellsep \tabcellsep \tabcellsep \\
Source\tabcellsep \tabcellsep \tabcellsep DF\tabcellsep \multicolumn{2}{l}{Adjusted}\tabcellsep Adjusted\tabcellsep F-Value\tabcellsep P-Value\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep SS\tabcellsep \tabcellsep MS\\
Speed\tabcellsep \tabcellsep \tabcellsep 1\tabcellsep 0.0163\tabcellsep \tabcellsep 0.01630\tabcellsep 0.24\tabcellsep 0.623\\
\multicolumn{2}{l}{Condition}\tabcellsep \tabcellsep 2\tabcellsep \multicolumn{2}{l}{15.3869}\tabcellsep 7.69346\tabcellsep 114.42\tabcellsep 0.000\\
\multicolumn{3}{l}{Speed*Condition}\tabcellsep 2\tabcellsep 0.1135\tabcellsep \tabcellsep 0.05675\tabcellsep 0.84\tabcellsep 0.432\\
Error\tabcellsep \tabcellsep \tabcellsep 174\tabcellsep \multicolumn{2}{l}{11.6990}\tabcellsep 0.06724\\
Total\tabcellsep \tabcellsep \tabcellsep 179\tabcellsep \multicolumn{2}{l}{27.2158}\\
\multicolumn{3}{l}{Model Summary}\tabcellsep \tabcellsep \tabcellsep \\
S\tabcellsep \multicolumn{2}{l}{R-sq}\tabcellsep \multicolumn{2}{l}{R-sq(adj) R-sq(pred)}\tabcellsep \\
\multicolumn{3}{l}{0.259299 57.01\%}\tabcellsep 55.78\%\tabcellsep 54.00\%\tabcellsep \\
\multicolumn{2}{l}{Coefficients}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
Term\tabcellsep \tabcellsep Coef\tabcellsep \multicolumn{4}{l}{SE Coef T-Value P-Value VIF}\\
\multicolumn{2}{l}{Constant}\tabcellsep \multicolumn{2}{l}{3.1936 0.0193}\tabcellsep \multicolumn{2}{l}{165.24 0.000}\\
Speed\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
1\tabcellsep \tabcellsep \multicolumn{2}{l}{-0.0095 0.0193}\tabcellsep -0.49\tabcellsep 0.623\tabcellsep 1.00\\
\multicolumn{2}{l}{Condition}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
11\tabcellsep \tabcellsep \multicolumn{2}{l}{0.4083 0.0273}\tabcellsep 14.94\tabcellsep 0.000\tabcellsep 1.33\\
12\tabcellsep \tabcellsep \multicolumn{2}{l}{-0.1474 0.0273}\tabcellsep -5.39\tabcellsep 0.000\tabcellsep 1.33\\
\multicolumn{3}{l}{Speed*Condition}\tabcellsep \tabcellsep \tabcellsep \\
1 11\tabcellsep \tabcellsep \multicolumn{2}{l}{0.0110 0.0273}\tabcellsep 0.40\tabcellsep 0.687\tabcellsep 1.33\\
1 12\tabcellsep \tabcellsep \multicolumn{3}{l}{-0.0347 0.0273 -1.27}\tabcellsep 0.205\tabcellsep 1.33\\
\multicolumn{3}{l}{Regression Equation}\tabcellsep \tabcellsep \tabcellsep \\
\multicolumn{7}{l}{Ra = 3.1936 -0.0095 Speed\textunderscore 1 + 0.0095 Speed\textunderscore 2 + 0.4083 Condition\textunderscore 11 -0.1474 Condition\textunderscore 12}\\
\multicolumn{7}{l}{-0.2608 Condition\textunderscore 13 + 0.0110 Speed*Condition\textunderscore 1 11 -0.0347 Speed*Condition\textunderscore 1 12}\\
\multicolumn{7}{l}{+ 0.0237 Speed*Condition\textunderscore 1 13 -0.0110 Speed*Condition\textunderscore 2 11 + 0.0347 Speed*Condition\textunderscore 2}\\
\multicolumn{5}{l}{12 -0.0237 Speed*Condition\textunderscore 2 13}\tabcellsep \\
\multicolumn{6}{l}{Fits and Diagnostics for Unusual Observations}\\
Obs.\tabcellsep Ra\tabcellsep Fit\tabcellsep Resid.\tabcellsep \multicolumn{2}{l}{Std. Resid.}\\
\multicolumn{5}{l}{21 3.0340 3.6034 -0.5694 -2.23 R}\tabcellsep \\
\multicolumn{4}{l}{30 2.9780 3.6034 -0.6254}\tabcellsep -2.45 R\tabcellsep \\
\multicolumn{4}{l}{33 3.5960 3.0019 0.5941}\tabcellsep 2.33 R\tabcellsep \\
\multicolumn{4}{l}{62 3.4700 2.9470 0.5230}\tabcellsep 2.05 R\tabcellsep \\
\multicolumn{4}{l}{150 3.6720 3.0904 0.5816}\tabcellsep 2.28 R\tabcellsep \\
\multicolumn{4}{l}{179 3.5330 2.9186 0.6144}\tabcellsep 2.41 R\tabcellsep \\
\multicolumn{3}{l}{R Large residual}\tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_4}General Linear Model: Ra versus Speed, Condition}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{42} \par 
\begin{longtable}{P{0.051802096985583225\textwidth}P{0.6890235910878112\textwidth}P{0.036205766710353866\textwidth}P{0.0005570117955439057\textwidth}P{0.028964613368283095\textwidth}P{0.0194954128440367\textwidth}P{0.014482306684141548\textwidth}P{0.002785058977719528\textwidth}P{0.0066841415465268665\textwidth}}
\tabcellsep \multicolumn{6}{l}{General Linear Model: Ra versus Speed, Condition}\\
Year 2018\tabcellsep \multicolumn{3}{l}{Analysis of Variance Source DF}\tabcellsep \multicolumn{2}{l}{Adjusted SS}\tabcellsep \multicolumn{2}{l}{Adjusted MS F-Value}\tabcellsep P-Value\\
12\tabcellsep \multicolumn{2}{l}{Speed}\tabcellsep 1\tabcellsep \multicolumn{2}{l}{1.6182}\tabcellsep 1.61824\tabcellsep 44.59\tabcellsep 0.000\\
J ( ) Volume XVIII Issue III Version I Global Journal of Researches in Engineering\tabcellsep \multicolumn{7}{l}{Condition Speed*Condition 2 2 Error 174 Total 179 Model Summary S R-sq R-sq(adj) R-sq(pred) 19.4964 0.1675 6.3147 27.5968 0.190503 77.12\% 76.46\% 75.51\% Coefficients Term Coef SE Coef T-Value P-Value VIF 9.74819 268.61 0.08374 2.31 0.03629 Constant 3.0778 0.0142 216.76 0.000 Speed 1 -0.0948 0.0142 -6.68 0.000 1.00 Condition 11 0.4598 0.0201 22.90 0.000 1.33 12 -0.1676 0.0201 -8.34 0.000 1.33 Speed*Condition 1 11 0.0426 0.0201 2.12 0.035 1.33 1 12 -0.0273 0.0201 -1.36 0.176 1.33 Regression Equation Ra = 3.0778 -0.0948 Speed\textunderscore 1 + 0.0948 Speed\textunderscore 2 + 0.4598 Condition\textunderscore 11 -0.1676 Condition\textunderscore 12 0.000 0.103 -0.2923 Condition\textunderscore 13 + 0.0426 Speed*Condition\textunderscore 1 11 -0.0273 Speed*Condition\textunderscore 1 12 -0.0153 Speed*Condition\textunderscore 1 13 -0.0426 Speed*Condition\textunderscore 2 11 + 0.0273 Speed*Condition\textunderscore 2 12 + 0.0153 Speed*Condition\textunderscore 2 13 Fits and Diagnostics for Unusual Observations Obs. Ra Fit Resid Std Resid 5 3.0070 3.4854 -0.4784 -2.55 R 21 3.9090 3.4854 0.4236 2.26 R}\\
\tabcellsep 23\tabcellsep \multicolumn{2}{l}{2.9400 3.4854}\tabcellsep -0.5454\tabcellsep -2.91 R\tabcellsep \\
\tabcellsep 27\tabcellsep \multicolumn{2}{l}{3.0900 3.4854}\tabcellsep -0.3954\tabcellsep -2.11 R\tabcellsep \\
\tabcellsep 92\tabcellsep \multicolumn{2}{l}{3.1680 3.5898}\tabcellsep -0.4218\tabcellsep -2.25 R\tabcellsep \\
\tabcellsep 112\tabcellsep \multicolumn{2}{l}{3.1950 3.5898}\tabcellsep -0.3948\tabcellsep -2.11 R\tabcellsep \\
\tabcellsep 120\tabcellsep \multicolumn{2}{l}{3.1150 3.5898}\tabcellsep -0.4748\tabcellsep -2.54 R\tabcellsep \\
\tabcellsep \multicolumn{2}{l}{R Large residual}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep © 2018 Global Journals\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_5}Table 4 . 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_6}Table}\end{figure}
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