Question

Consider the following data:

X	Y
1	13
3	10
5	9
5	5
6	3

1. Draw a Scatter Plot of the data.
2. Do you believe the correlation coefficient r will be positive, negative or close to zero? Why
3. What is your estimate to the value of Y associated with X=4?

Answer 1

x=c(1,3,5,5,6)
y=c(13,10,9,5,3)
# a) scatter plot
plot=plot(x,y)


#b)
> data=data.frame(x,y)
> data
x y
1 1 13
2 3 10
3 5 9
4 5 5
5 6 3
model=lm(y~x,data=data)
>model

Call:
lm(formula = y ~ x, data = data)

Coefficients:
(Intercept) x
15.250 -1.812

R_squared=summary(model)$r.squared
R_squared
[1] 0.8212891
correlation_coefficent=sqrt(R_squared)
correlation_coefficent
[1] 0.90625

here correlation coefficent is postive quantity hence it is postive and close to one

#c) our fitted model is Y^=15.250-1.812*x
x=4
y_pred=15.250-1.812*4
y_pred
[1] 8.002

here Y associated with x=4 is  8.002