SOLUTION: The following are the scores of 15 students obtained in the midterm and final examinations in a course in probability and statistics Midterm Exam, x 70 50 80 75 90 85 60 80

Question 1011186: The following are the scores of 15 students obtained in
the midterm and final examinations in a course in
probability and statistics
Midterm
Exam, x 70 50 80 75 90 85 60 80 65 30 85 80 70 65 40
Final
Exam, y 85 60 75 80 90 75 50 75 75 50 75 90 65 55 60
(i) Find the equation of the least square line to fit these
data,
(ii) Estimate the final examination scores of a student
who received a score of 74 in the midterm
examination.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Steps in using least square method
1) calculate the mean of the x values (midterm grade)
2) calculate the mean of the y values (final grade)
3) calculate the slope of the line of best fit
slope = (summation from i = 1 to 15 of (xi - xmean)*(yi - ymean)) / (summation of i = 1 to 15 of (xi - xmean)^2)
4) compute the y intercept using
b = ymean - (slope*xmean)
5) you now have the equation of the line using least square method
*******************************************************************************
1) xmean = 68.33
2) ymean = 70.67
3) slope = 2466.67 / 4183.33 = 0.59
4) b = 70.67 - (0.59 * 68.33) = 30.36
5) y = 0.59x + 30.36
now if x = 74 then
y = (0.59*74) + 30.36 = 74.02
using our line using least square method, we expect a student who gets a 74 on the midterm to get a 74 on the final

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