Question

QUESTION 1 Find the equation of the regression line. x | 52 60 54 53 5556 y1308 338 308 298 298 308 aragraph M Arial M 3 (12pt) ?I :-- E-Ti, Path Click Save and Submit to save and submit Click Save A Anstwers to save all answers

Answer 1

Solution

Back-up Theory

The linear regression model Y = ?₀ + ?₁X + ?, ………………………………………..(1)

where ? is the error term, which is assumed to be Normally distributed with mean 0 and variance ?².

Estimated Regression of Y on X is given by: Y = ?_0cap + ?_1capX, ………………………….(2)

where

?_1cap = Sxy/Sxx and ?_0cap = Ybar – ?_1cap.Xbar..……………………………………………..(3)

Mean X = Xbar = (1/n)sum of x_i ………………………………………….……………….(4)

Mean Y = Ybar = (1/n)sum of y_i ………………………………………….……………….(5)

Sxx = sum of (x_i – Xbar)^{2 …………………………………………………..}………………………………..(6)

Syy = sum of (y_i – Ybar)^{2 …………………………………………………..}………………………………..(7)

Sxy = sum of {(x_i – Xbar)(y_i – Ybar)} ^{…………………………………………………………………….}………(8)

All above sums are over i = 1, 2, …., n

n = sample size ………………………………………………………………………………(9)

Calculations:

Given data

i	xi	yi
1	52	308
2	60	338
3	54	308
4	53	298
5	55	298
6	56	308

Summary of Excel Calculations

n	6
xbar	55
ybar	309.6667
Sxx	40
Syy	1083.3333
Sxy	170
?1cap	4.25
?0cap	75.9167

Thus, the regression equation is: y = 75.92 + 4.25x ANSWER

DONE