The following table shows how many weeks a sample of 6 persons have worked at an

Question

The following table shows how many weeks a sample of 6 persons have worked at an automobile inspection station and the number of cars each person inspected between noon and 2:00pm on any given day: a) Obtain the least spaces fit equation of a straight line to the amount of additive, using the least squared estimators. b) Use the equation of the least squares line to estimate mean number of can inspected at number of weeks employed, x = 11. c) Find the correlation coefficient, r, and describe the relationship between number of weeks employed and number of can inspected.

Explanation / Answer

a)

b1= nE(xy)-ExEy/nE(x2)-(Ex2)

= 6(711)-(36)(108)/ 6*304-(36)2

= 0.7159

b0= Ey-b1Ex/n

= 108-(0.7159)(36)/6

= 13.7046

y=13.7046+0.7159x

b)

y=13.7046+0.7159x

=13.7046+0.7159(11)

=13.7046+0.7159(11)

=13.7046+7.875

=21.5796

c)

r (correlation)=n(Exy)-(Ex)(Ey)/sqrt(nEx2-(Ex)2)(nEy2-(Ey)2)

=6(711)-(36)(108)/(6*304-(36)^2)(6*2080-(108)^2)

=0.5758

Number of weeks employed, X Number of cars inspected, Y X^2 Y^2 XY 2 13 4 169 26 7 21 49 441 147 9 25 81 625 225 1 18 1 324 18 5 11 25 121 55 12 20 144 400 240 36 108 304 2080 711

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