## Problem 3 # Here is a data vector that will be used in this problem. vec = c(3, -4, 0, 12, 23, 26) # Please don't change the values of this vector (the autograder has a copy of these values that it uses) # a vector x with length 6 so that the correlation between x and vec is exactly +1 # Hint: This means vec and x have a perfect linear relationship with a positive slope x = c(vec) # Hint: You can calculate the correlation between x and vec to check your answer. This will give you more information for any adjustments you need to make. # a vector y with length 6 so that the correlation between y and vec is exactly -1 y = c(-vec) # a vector z with length 6 so that the correlation between z and vec is close to 0. # Any correlation between -0.3 and +0.3 will be accepted by the autograder for this part. z = c()

# a vector w with length 6 so that the correlation between w and vec is between -0.9999 and -0.7 # Note a correlation of -1 is not accepted for this part, but anything between -0.9999 and -0.7 is accepted. w = c() # a vector v with length 6 so that the correlation between v and vec is between +0.3 and +0.7

v = c()

The correlation between z and vec is approximately -0.20, which is within the acceptable range of -0.3 to +0.3, indicating a very low or negligible linear relationship. The correlation between w and vec is approximately -0.99999, which falls within the specified range of -0.9999 to -0.7, indicating a very strong negative linear relationship but not a perfect one. The correlation between v and vec is approximately 0.77, which is slightly outside the specified range of +0.3 to +0.7. We aimed for a correlation within this range, so I'll adjust the variability in v to correct this.

Please fill in the codes for z, w, v while retaining the "= c()" format. and check if x and y are correct