Question

3. (26 pts.) The damping ratio ( y ) of a polymer material is measured at various temperatures (x) as shown in the table below. Temperature (°C), x, Damping ratio (%), y, у 10 20 30 15 0 10 20 30 40 (1) (14 pts.) Determine the regression equation of y on x in the form, y = a +bx. (So, you need to determine a and b.) (2) (2 pts.) Determine the centroidal point. (3) (2 pts.) Show that the best-fit line (y = a +bx) passes through the centroidal point. (4) (2 pts.) Calculate the correlation coefficient, R, for this data set. (5) (2 pts.) Calculate the coefficient of determination, R. (6) (2 pts.) Determine Že, where e = y;-(a+bx ) (7) (2 pts.) Determine SS

Answer 1

Ans Here first variable x as follows. we with prepare pmf the and table of require random quantity 15000 P(2) RPC) e. Por २/२82-128 5/28 10/28 8/28 24/28 6/08 24/28 20/28 ___18/28 x? Podl 2/28 20/28 १२/28 96/28 100/28 108/28 4/28 328 Total 98/28 398/28 1 TO Find P(X = - is even) (x2) +P(x +4) + PCX56) 5 +: + 3 28 28 28 २8 र i cx is even) = 0.5

a ý - b = 11- 0.35 x 20 I a=4 Hence Regression equation yon tis. Y = 4 +0.35% ② point is: The centroidal (X,Y)= (20,10) . line pass through Now to show that the centroida let X=20 Y = 4+0.35 x 20 Hence. If = 4 +0.35% line pass through the Hence best centroidal fit point? R = correlation coefficient EXY - XY WEX,2-nx2)(VEY, 2-n92) - 730 - 3x11x20 N1400-3X202 389-3x112 = 70 200x260 70 5200 R=0.97072 Ics-Scanned with CamScanner

6 Coefficient of determination = R² R² = 0.97072 R2= 0.9423 - Now to determin. isi eo - yo-(a+bxo). yo Taxi atbai е , 705 I 05. 20 14.5 0.5 10 30 i= ei 0.5-1 +0.5 ol = = 0.52 + (-1)2 +0.s? 1.5 SSE Scanned with CamScanner