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
Algebra.Com
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): You can put this solution on YOUR website!
X2 refers to X^2 or
Y2 refers to Y^2 or
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
\left(\sum \text{x}^2\right)-\left(\sum \text{x}\right)\left(\sum \text{x}\text{y}\right)}{n\left(\sum \text{x}^2\right) - \left(\sum \text{x}\right)^2)
-\left(\sum \text{x}\right)\left(\sum \text{y}\right)}{n\left(\sum \text{x}^2\right) - \left(\sum \text{x}\right)^2)
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
*(130)-(32)*(2136)}{8(130)-(32)^2})
Now onto the slope
 - (32)*(528)}{8(130)-(32)^2})
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
RELATED QUESTIONS
A random sample of 8 applicants for a certain foreign job is selected. The number of... (answered by math_tutor2020,ikleyn)
A random sample of 8 applicants for a certain foreign job is selected. The number of... (answered by MathLover1)
Forty percent of job applicants are rejected. In a random sample of 12 applicants: what... (answered by Edwin McCravy)
Forty percent of job applicants are rejected in a random sample of 12 applicants, what is (answered by ewatrrr)
there is an 80% chance that a prospective employer will check the educational background... (answered by stanbon)
At a company, the data set containing the ages of the applicants for a particular job was (answered by Boreal)
Among 120 applicants for a job in an insurance company, only 80 are actually qualified.... (answered by ikleyn)
you are told that there is an 80% chance that a prospective employer will check the... (answered by Boreal,mathmate)
Please show me how to do this. The book I am using doesn't provide enough example for me... (answered by stanbon)