a)
|
x |
y |
(x-x?)² |
(y-y?)² |
(x-x?)(y-y?) |
|
24 |
76 |
1336.31 |
2928.01 |
1978.06 |
|
32 |
58 |
815.42 |
5200.01 |
2059.17 |
|
75 |
190 |
208.64 |
3586.68 |
865.06 |
|
41 |
112 |
382.42 |
328.01 |
354.17 |
|
76 |
141 |
238.53 |
118.57 |
168.17 |
|
107 |
235 |
2157.09 |
11001.68 |
4871.51 |
|
32 |
24 |
815.42 |
11259.57 |
3030.06 |
|
46 |
147 |
211.86 |
285.23 |
-245.83 |
|
112 |
188 |
2646.53 |
3351.12 |
2978.06 |
|
|
?X |
?Y |
?(x-x?)² |
?(y-y?)² |
?(x-x?)(y-y?) |
| total
sum |
545 |
1171 |
8812.222222 |
38058.9 |
16058.44 |
|
mean |
60.56 |
130.11 |
SSxx |
SSyy |
SSxy |
correlation coefficient , r = Sxy/?(Sx.Sy)
= 0.877
b)
sample size , n = 9
here, x? = ?x / n= 60.56 ,
y? = ?y/n = 130.11
SSxx = ?(x-x?)² = 8812.2222
SSxy= ?(x-x?)(y-y?) = 16058.4
estimated slope , ß1 = SSxy/SSxx = 16058.4
/ 8812.222 = 1.8223
intercept, ß0 = y?-ß1* x? =
19.7612
so, regression line is Y? = 19.76
+ 1.82 *x
c)
Predicted Y at X= 108 is
Y? = 19.76119 +
1.822292 * 108
= 216.57
