ATM forecast process programming Time

Read in data:

atmruns<-read.table(header=TRUE, text="atms minutes
200 5.8
200 35.9
200 20.9
200 35.4
200 10.2
200 24.5
200 16.6
400 86.1
400 59.6
400 64.9
400 61.2
400 54.3
400 96.8
400 55.8
600 114
600 82.9
600 74
600 88.4
600 75.3
600 113.3
600 93.9
800 119.1
800 131.3
800 122
800 120
800 127
800 139.4
800 149.9
1000    175.1
1000    165.8
1000    214.4
1000    166.6
1000    145.4
1000    185
1000    160.2
")
head(atmruns)

Fit model and look at results

fit<-lm(minutes~atms,data=atmruns)
summary(fit)

Call:
lm(formula = minutes ~ atms, data = atmruns)

Residuals:
    Min      1Q  Median      3Q     Max 
-24.526 -10.566  -2.986   8.774  44.474 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept) -12.674286   6.389752  -1.984   0.0557 .  
atms          0.182600   0.009633  18.956   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 16.12 on 33 degrees of freedom
Multiple R-squared:  0.9159,    Adjusted R-squared:  0.9133 
F-statistic: 359.3 on 1 and 33 DF,  p-value: < 2.2e-16

plot the data:

plot(minutes~atms,data=atmruns)

Improving look of plot and adding fit line

plot(minutes~atms,data=atmruns,cex=1.5,cex.axis=1.5,cex.lab=1.5,pch=20)
abline(fit,col="blue",lwd=2)

Examine Results:

plot(fit)

Alternative method for graph enhancements:

Save function to extract equation for plot:

equation = function(x) {
  lm_coef <- list(a = round(coef(x)[1], digits = 2),
                  b = round(coef(x)[2], digits = 2),
                  r2 = round(summary(x)$r.squared, digits = 2));
  lm_eq <- substitute(italic(y) == a + b %.% italic(x)*","~~italic(R)^2~"="~r2,lm_coef)
  as.character(as.expression(lm_eq));                 
}

Add ggplot2 library

library(ggplot2);

Create Scatterplot

ggplot(atmruns, aes(x=atms, y=minutes)) +
  geom_point() +    
  geom_smooth(method=lm,  se=FALSE) +   
 ggtitle("Optimization Time for ATM Program") +
   annotate("rect", xmin = 615, xmax = 1025, ymin = 25, ymax = 50, fill="white", colour="red") +
  annotate("text", x = 820, y = 39, label = equation(fit), parse = TRUE)

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