SOLUTION: A random sample of 8 applicants for a certain foreign job is selected. The number of years that these applicants have studied French in high school or university, X, and the mark w

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Question 1196551: A random sample of 8 applicants for a certain foreign job is selected. The number of years that these applicants have studied French in high school or university, X, and the mark which they obtained in a proficiency test in French, Y, are recorded. The following information is given: ∑X =32, ∑Y =528, ∑XY=2136, ∑X2 =130 and ∑Y2 =34872 Fitting a regression line, which of the following statements is incorrect?

a.
b₁ = 12
b.
Ŷ = 12+18Xi
c.
The predicted mark obtained if an applicant studied French for two years is 42.
d.
b₀ = 18
e.
Mean of X values = 4 Mean of Y values = 66
Answer by math_tutor2020(3838) About Me  (Show Source):
You can put this solution on YOUR website!

X2 refers to X^2 or X%5E2
Y2 refers to Y^2 or Y%5E2

Given info:
n = 8 = sample size
∑X =32, ∑Y =528, ∑XY=2136, ∑X2 =130 and ∑Y2 =34872
Something like ∑X =32 means the X values add to 32.

The regression line is Ŷ = b₀ + b₁*Xi
b₀ = y intercept
b₁ = slope
This is a different way to express the slope-intercept form y = mx+b.

The formulas to compute each are




Notes:
  • The denominators are identical.
  • Since the formulas are ugly and complicated, it's best to use statistical or spreadsheet software when it comes to real world linear regression applications.
Let's compute the y intercept









Now onto the slope








The equation Ŷ = b₀ + b₁*Xi updates to Ŷ = 18+12Xi
Therefore, choice B is the incorrect statement. The 12 and 18 needed to be swapped around.

Answer: Choice B) Ŷ = 12+18Xi