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(3816) (Show Source):
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.
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