Assignment 33

x=c(3,5,2,3,1,4,6,4,3,0)
y=c(300,300,500,400,700,400,100,250,450,600)

plot(x,y,
     xlab="Oil Changes Per Year",
     ylab="Repair Costs",
     main="Repair Costs Compared to Amount of Oil Changes")

lm.res=lm(y~x)
abline(lm.res)

lm.res

## 
## Call:
## lm(formula = y ~ x)
## 
## Coefficients:
## (Intercept)            x  
##       673.5        -88.2

yhat=673.53-88.24*x
yhat

##  [1] 408.8 232.3 497.0 408.8 585.3 320.6 144.1 320.6 408.8 673.5

plot(x,y,
     pch=20,col="red",
     xlab="x=Oil Changes per Year",
     ylab="y=Repair Costs",
     main="Repair Costs Compared to Amount of Oil Changes")
abline(lm.res)
points(x,yhat,pch=15,col="green")

abline(h=0)

Based off of the plots shown the linear model does seem approproaite because the line of best fit matches the phat values.

data=read.delim("ldi13_4.dat",header=TRUE)
data

##    Time Distance      P      Q   RES_1
## 1  0.16     12.1 0.4000  75.62  42.283
## 2  0.24     29.8 0.4899 124.17  18.088
## 3  0.25     32.7 0.5000 130.80  15.751
## 4  0.30     42.8 0.5477 142.67  -0.334
## 5  0.30     44.2 0.5477 147.33   1.066
## 6  0.32     55.8 0.5657 174.38   2.192
## 7  0.36     63.5 0.6000 176.39 -11.056
## 8  0.36     65.1 0.6000 180.83  -9.456
## 9  0.50    124.6 0.7071 249.20 -23.273
## 10 0.50    129.7 0.7071 259.40 -18.173
## 11 0.57    150.2 0.7550 263.51 -34.332
## 12 0.61    182.2 0.7810 298.69 -23.280
## 13 0.61    189.4 0.7810 310.49 -16.080
## 14 0.68    220.4 0.8246 324.12 -21.739
## 15 0.72    254.0 0.8485 352.78  -9.086
## 16 0.72    261.0 0.8485 362.50  -2.086
## 17 0.83    334.6 0.9110 403.13  13.907
## 18 0.88    375.5 0.9381 426.70  28.622
## 19 0.89    399.1 0.9434 448.43  46.985

D=data$Distance
T=data$Time

plot(T,D,col="red",
     xlab="Time",
     ylab="Distance",
     main="Distance Fallen Compared to Time")

lm.res=lm(D~T)
abline(lm.res)

lm.res

## 
## Call:
## lm(formula = D ~ T)
## 
## Coefficients:
## (Intercept)            T  
##        -114          524

yhat=-114+523.7*x
yhat

##  [1] 1457.1 2504.5  933.4 1457.1  409.7 1980.8 3028.2 1980.8 1457.1 -114.0

plot(x,y,
     pch=20,col="blue",
     xlab="x=Time",
     ylab="y=Distance",
     main="Distance Fallen Compared to Time")

abline(lm.res)
points(x,yhat,pch=15,col="purple")

P=sqrt(T)
plot(P,D)
lm.res=lm(D~P)
abline(lm.res)

Q=D/T
plot(T,Q)
lm.res=lm(Q~T)
abline(lm.res)

Based off of these plots a linear model doesn’t seem appropriate.

Q and T seem to have the closest to a linear relationship.