Model for Estimating The performence of Computer
Prabha Shankar
December 27, 2017
1. Introduction
This project deals with estimating the performence of Computer using the data source from https://archive.ics.uci.edu/ml/datasets/Computer+Hardware . The creator of the data set is Phillip Ein-Dor and Jacob Feldmesser(Faculty of Management, Tel Aviv University, Ramat-Avi Tel Aviv, 69978 ,Israel) . Data set contain 209 instanses having 9 attributes .
This paper addresses the following issues concerning the “Performence of computer” with respect to the computer hardware. In this Paper We evaluate whether their is difference between the published relative performence and estimeted relative performence and estimating the relative performence of the computer using regression model .
Read the data
setwd("C:/Users/Prabha Shankar/Desktop/Winter Internship/Project")
var1.df <- read.table("machine.data", header = FALSE , sep = ",")
colnames(var1.df) <- c("v_name","M_name","MYCT","MMIN","MMAX","CACH","CHMIN","CHMAX","PRP","ERP")Dimension of Data
dim(var1.df)## [1] 209 10Frequency of all the vendors
table(var1.df$v_name)##
## adviser amdahl apollo basf bti
## 1 9 2 2 2
## burroughs c.r.d cambex cdc dec
## 8 6 5 9 6
## dg formation four-phase gould harris
## 7 5 1 3 7
## honeywell hp ibm ipl magnuson
## 13 7 32 6 6
## microdata nas ncr nixdorf perkin-elmer
## 1 19 13 3 3
## prime siemens sperry sratus wang
## 5 12 13 1 2library(psych)## Warning: package 'psych' was built under R version 3.3.3Mean , Median And Standard Deviation of Variables
describe(var1.df)[(3:10),c(1:5)]## vars n mean sd median
## MYCT 3 209 203.82 260.26 110
## MMIN 4 209 2867.98 3878.74 2000
## MMAX 5 209 11796.15 11726.56 8000
## CACH 6 209 25.21 40.63 8
## CHMIN 7 209 4.70 6.82 2
## CHMAX 8 209 18.27 26.00 8
## PRP 9 209 105.62 160.83 50
## ERP 10 209 99.33 154.76 45boxplot(var1.df$MYCT, data=var1.df, main="Percentage of machine cycle ", xlab="Percentage of machine cycle", ylab="", horizontal=TRUE )
boxplot(var1.df$CHMAX, data=var1.df, main="Percentage of minimum main memory ", xlab="Percentage of Menimum memory", ylab="", horizontal=TRUE )
boxplot(var1.df$MMAX, data=var1.df, main="Percentage of maximum main memory ", xlab="Percentage of Maximum main memory", ylab="", horizontal=TRUE )
boxplot(var1.df$CACH, data=var1.df, main="Percentage of cach memory ", xlab="Percentage of cach memory", ylab="", horizontal=TRUE )
boxplot(var1.df$CHMIN, data=var1.df, main="Percentage of minimum channels ", xlab="Percentage of Minimum Channels", ylab="", horizontal=TRUE )
boxplot(var1.df$CHMAX, data=var1.df, main="Percentage of maximum channels ", xlab="Percentage of Maximum Channels", ylab="", horizontal=TRUE )
boxplot(var1.df$PRP, data=var1.df, main="Percentage of published relative performence ", xlab="Percentage of published relative performence", ylab="", horizontal=TRUE )
hist(var1.df$PRP,xlab="Published Relative Performence" ,main="Distribution of PRP")
The PRP Value is continuously valued .
Corelation TEst
library(car)## Warning: package 'car' was built under R version 3.3.3##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitcorelation Test between minimum main memory and estimated relative performence
cor.test(var1.df$MMIN,var1.df$ERP)##
## Pearson's product-moment correlation
##
## data: var1.df$MMIN and var1.df$ERP
## t = 20.558, df = 207, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.7690922 0.8594446
## sample estimates:
## cor
## 0.8192915Graphical representation
scatterplot(var1.df$MMIN,var1.df$ERP)
corelation Test between maximum main memory and estimated relative performence
cor.test(var1.df$MMAX,var1.df$ERP)##
## Pearson's product-moment correlation
##
## data: var1.df$MMAX and var1.df$ERP
## t = 29.917, df = 207, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8721582 0.9239162
## sample estimates:
## cor
## 0.9012024Graphical Representation
scatterplot(var1.df$MMAX,var1.df$ERP)
corelation Test between cach memory and estimated relative performence
cor.test(var1.df$CACH,var1.df$ERP)##
## Pearson's product-moment correlation
##
## data: var1.df$CACH and var1.df$ERP
## t = 12.261, df = 207, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.5624133 0.7208780
## sample estimates:
## cor
## 0.6486203Graphical Representation
scatterplot(var1.df$CACH,var1.df$ERP)
corelation Test between minimum channels and estimated relative performence
cor.test(var1.df$CHMIN,var1.df$ERP)##
## Pearson's product-moment correlation
##
## data: var1.df$CHMIN and var1.df$ERP
## t = 11.092, df = 207, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.5177705 0.6891857
## sample estimates:
## cor
## 0.6105802Graphical Representation
scatterplot(var1.df$CHMIN,var1.df$ERP)
corelation Test between maximum channels and estimated relative performence
cor.test(var1.df$CHMAX,var1.df$ERP)##
## Pearson's product-moment correlation
##
## data: var1.df$CHMAX and var1.df$ERP
## t = 10.573, df = 207, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.4963279 0.6737267
## sample estimates:
## cor
## 0.5921556Graphical Representation
scatterplot(var1.df$CHMAX,var1.df$ERP)
corelation Test between published relative performence and estimated relative performence .
cor.test(var1.df$PRP,var1.df$ERP)##
## Pearson's product-moment correlation
##
## data: var1.df$PRP and var1.df$ERP
## t = 54.153, df = 207, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.9561728 0.9743821
## sample estimates:
## cor
## 0.9664717Graphical Representation
scatterplot(var1.df$PRP,var1.df$ERP)
value of corelation between variables.
round(cor(var1.df[, 3:10], use="pair"),2)## MYCT MMIN MMAX CACH CHMIN CHMAX PRP ERP
## MYCT 1.00 -0.34 -0.38 -0.32 -0.30 -0.25 -0.31 -0.29
## MMIN -0.34 1.00 0.76 0.53 0.52 0.27 0.79 0.82
## MMAX -0.38 0.76 1.00 0.54 0.56 0.53 0.86 0.90
## CACH -0.32 0.53 0.54 1.00 0.58 0.49 0.66 0.65
## CHMIN -0.30 0.52 0.56 0.58 1.00 0.55 0.61 0.61
## CHMAX -0.25 0.27 0.53 0.49 0.55 1.00 0.61 0.59
## PRP -0.31 0.79 0.86 0.66 0.61 0.61 1.00 0.97
## ERP -0.29 0.82 0.90 0.65 0.61 0.59 0.97 1.00Graphical Representation.
scatterplot.matrix(~ERP+MYCT+MMIN+MMAX+CACH+CHMIN+CHMAX+PRP, data=var1.df)## Warning: 'scatterplot.matrix' is deprecated.
## Use 'scatterplotMatrix' instead.
## See help("Deprecated") and help("car-deprecated").
T_Test
Null Hypothesis (H0) : There is no difference between Published Relative Performence and Estimated Relative performence (ERP) .
t.test(var1.df$PRP,var1.df$ERP,var.equal = TRUE ,paired = FALSE)##
## Two Sample t-test
##
## data: var1.df$PRP and var1.df$ERP
## t = 0.40754, df = 416, p-value = 0.6838
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -24.05585 36.63958
## sample estimates:
## mean of x mean of y
## 105.62201 99.33014Since the p-value is significantly larger than 0.05 , therfore we will accept the null hypothesis and reject the alternative hypothesis . Hence there is no difference between PRP and ERP .
T_TEst
Null Hypothesis (H0) : value of estimated relative performence of computer not depends on anoter factor
t.test(var1.df$ERP,var.equal = TRUE ,paired = FALSE)##
## One Sample t-test
##
## data: var1.df$ERP
## t = 9.2791, df = 208, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
## 78.22638 120.43390
## sample estimates:
## mean of x
## 99.33014Since the p-value is significantly less than 0.05, therfore we will reject he null hypothesis . Hence the estimateed relative performence (ERP) depends on seeral factors . To find that we will perform regression analysis .
REGRESSION
Formulating multivariate linear regression model to ???t Performence of computer with respect to the model selection .
IndependentVariables: {MYCT,MMIN,MMAX,CACH,CHMIN,CHMAX,PRP}
Dependent Variable: ERP
Model <- ERP ~ MYCT+MMIN+MMAX+CACH+CHMIN+CHMAX+PRP
fit <- lm(Model, data = var1.df)
summary(fit)##
## Call:
## lm(formula = Model, data = var1.df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -117.478 -9.546 2.864 15.257 182.251
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3.423e+01 4.732e+00 -7.234 9.68e-12 ***
## MYCT 3.777e-02 9.434e-03 4.004 8.77e-05 ***
## MMIN 5.483e-03 1.120e-03 4.894 2.02e-06 ***
## MMAX 3.375e-03 3.974e-04 8.493 4.45e-15 ***
## CACH 1.244e-01 7.751e-02 1.605 0.11016
## CHMIN -1.634e-02 4.523e-01 -0.036 0.97122
## CHMAX 3.458e-01 1.287e-01 2.687 0.00781 **
## PRP 5.770e-01 3.718e-02 15.519 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 31.7 on 201 degrees of freedom
## Multiple R-squared: 0.9595, Adjusted R-squared: 0.958
## F-statistic: 679.5 on 7 and 201 DF, p-value: < 2.2e-16Result
- There is not that much difference between the Published relative performence and estimated relative performence .
2.The model we get for estimating the ERP is .