Pleasse answer C & D with out using Matlab or a graphic calculator. please ident
ID: 3362270 • Letter: P
Question
Pleasse answer C & D with out using Matlab or a graphic calculator. please identify any formulas used
8. The following information was obtained from a random sample of sixteen professional engineers. The variable X represents the years of job-related experience, while the variable Y represents the annual remuneration in thousands of dollars. It X, = 384.0 y2 = 10,716.0 =2,496.0; , 391,536.0 .XX = 61.254.0 (a) Compute (i) the covariance of X and Y and (ii) the coefficient of correlation r of X and Y (b) Find the 95% confidence limits of the true coefficient of correlation (c) It is believed that Y and X are related by an equation of the form Y-Bo + + Write down the normal equations of the least squares line and then compute the estimates bo and bl of 0 and 1 respectively. (d) Compute the error sum of squares and use this information to find the 95% confidence limits of 1.Explanation / Answer
C)
Y = nB0 + B1 x
XY = B0x + B1 x2
Calculations
2496 = 16*B0 + B1 * 384
61.254 = B0 * 384 + B1 * 10716
By solving these equations
we get B0 = 1113.48
B1 = -39.8952
Now required regression equation
Y = 1113.48 - 39.8952*X
d) Error sum of squares
[Y - Ybar]2
=> Y2 + n*Ybar2 - 2 Y*Ybar
=> 391536 + 16*(2496/16)2 - 2*391536/16
=> 731970