Question

1. In the following table of paired data the variable x represents the opening

bid suggested by an auctioneer and y represents the final winning bid for

several items.

x 1500 500 450 400 300

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y 750 550 125 275 125

Find the equation of the regression line for the data in Problem 1. Round your slope and y-intercept to three decimal places.

2. Use your regression line equation to predict the final bid

on an item with suggest opening bid $425.

Round your answer to the nearest whole number.

Answer 1

Solution:
slope of the regression euqation can be calculated as
b = n*summation(X*Y) - Summation(X)*summartion(Y) / n*summation(X^2) - (summation(X))^2

X	Y	X*Y	X^2	Y^2
1500	750	1125000	2250000	562500
500	550	275000	250000	302500
450	125	56250	202500	15625
400	275	110000	160000	75625
300	125	37500	90000	15625
3150	1825	1603750	2952500	971875

b = 5*1603750 - (3150*1825) / (5*2952500 -3150*3150)
b = 2270000/4840000 = 0.4690
Intercept can be calculated as
a = summation(Y) - b*Summation(X) / n
a = (1825 -(0.4690*3150))/5 = (1825 - 1477.37) /5 = 69.52

So linear regression equation is
Y = a +bX
Y = 69.524 + 0.469 *X

Solution(2)
Given X = 425
SO Y = 69.524 + 0.469*425 = 69.524 + 199.325 = 268.849 or 269
So final bid on an item with sugget opening bid $425 is 269