Consider the following data sample data obtained in a study of relationship between the number of that applicants for a certain foreign service jobs have studied German in high school or college and the grades that they received on a proficiency test in that language.

# of years(x)	2	3	4	5
Grade in test(y)	58, 48	57, 63, 75	78, 72, 73	89, 84

Some calculations:

∑x = 35, ∑x ² = 133, ∑y = 697, ∑y ² = 50085 and ∑xy = 2554

a) Fit a k-at squares line to the data.

b) Find the residual for the 9th applicant's data.

c) Based on the data, error standard deviation is found to be 5.65. Test the hypothesis that each additional year in German in high school or college ads another 12.5 point to the expected proficiency score of an applicant. Use the alternative hypothesis β ₁ ≠12.5 and level of significance 0.05.