Question

2. The following data (stored in Drink) represent the amount of soft drink in a sample of 50 consecutively filled 2-liter bottles. The results are listed horizontally in the order of being filled:

2.109 2.086 2.066 2.075 2.065 2.057 2.052 2.044 2.036 2.038

2.031 2.029 2.025 2.029 2.023 2.020 2.015 2.014 2.013 2.014

2.012 2.012 2.012 2.010 2.005 2.003 1.999 1.996 1.997 1.992

1.994 1.986 1.984 1.981 1.973 1.975 1.971 1.969 1.966 1.967

1.963 1.957 1.951 1.951 1.947 1.941 1.941 1.938 1.908 1.894

a Construct a line chart for the amount of soft drink on the Y axis and the bottle number (going consecutively from 1 to 50) on the X axis.

b What pattern, if any, is present in these data?

c If you had to make a prediction about the amount of soft drink filled in the next bottle, what would you predict?

Answer 1

a.

b. From above plot, we see that as bottle no. increases, amount of soft drink decreases. Since correlation coefficient between two variables=-0.9725 which is very strong negative correlation. Hence we can consider these two variables are linearly associated.

c. Predicted amount of soft drink filled in the next bottle=1.925

R code:

y=c(2.109,2.086,2.066,2.075,2.065,2.057,2.052,2.044,2.036,2.038,2.031,2.029,
2.025,2.029,2.023,2.020,2.015,2.014,2.013,2.014,2.012,2.012,2.012,2.010,2.005,
2.003,1.999,1.996,1.997,1.992,1.994,1.986,1.984,1.981,1.973,1.975,1.971,1.969,
1.966,1.967,1.963,1.957,1.951,1.951,1.947,1.941,1.941,1.938,1.908,1.894)
plot(y,type ="o",col="2",xlab="bottle number",ylab="Amount of soft drink")#(a)
x=1:50
round(cor(x,y),4)#(b)
m=lm(y~x)
new=data.frame(x=51)
round(predict(m,new),3)#(c)