near regression equation
17.3 the frequency of electrical impulses emitted from electric fish is measured from fish at different temperatures. The resultant data are as follows:
|
temperature © |
Impulse frequency (number/sec |
ni |
|
225,230,239 |
3 | |
|
22 |
251,259,265 |
3 |
|
23 |
266,273,280 |
3 |
|
25 |
287,295,302 |
3 |
|
27 |
301,310,317 |
3 |
|
28 |
307,313,325 |
3 |
|
30 |
324,330,338 |
3 |
(a) Compute a and b for the linear regression equation relation impulse frequency to temperature. (b) test, by analysis of variance, H0:β = 0. (c) calculate the standard error of estimate of the regression. (d) calculate the coefficient of determination of the regression. (e) test H0: the population regression is linear.
N = 21
∑∑ xij = 525 ∑∑ yij =6037 ∑∑xijyij =153143
∑∑xi2j = 13353 ∑∑yi2j =1758389 ∑xy = 2218
b = = =9.728
a = - b =287.47 - 9.728(25) = 44.27
therefore, the least squares regression lin is = 44.27 + 9.728 xij
H0: the population regression is linear.
HA: the population regression is not linear.
Ss total: ∑∑yi2j - = 1758389 - = 22895.238
among groups ss = - = - =22089.9
among groups DF k-1 = 6
Within groups ss = total ss - among groups ss = 22895.238 - 22089.9 = 805.338
Within groups DF = total DF - among groups DF = 20 – 6 = 14
Regression ss = = = 21576.859
Deviations from linearity ss = among groups ss –regression ss = 22089.9 - 21576.859 =513.041 Deviations from linearity DF = among groups DF– regression DF = 6 – 1 = 5
Regression with replication: test for linearity
|
source of variation |
ss |
Df |
MS |
|
total |
22895.238 |
20 |
- |
|
among groups |
6 |
- | |
|
linear Regression |
21576.859 |
1 |
- |
|
513.041 |
5 |
||
|
805.338 |
14 |
||
|
F = = 1.78387 |
Since F >table F , do not reject H0
|
source of variation |
Ss |
Df |
MS |
|
total |
20 |
||
|
linear Regression |
1 |
||
|
residual |
1318.379 |
19 |
F = 310.995
Since F > table F , therefore reject H0
r 2= = 0.942
sy.x= = 8.329
1. Adjusment for random data that has a binonmal distribut?
|
73 |
45 |
3 | |
|
69 |
50 |
7 | |
|
80 |
42 |
4 | |
|
83 |
46 |
9 | |
|
74 |
48 |
2 | |
|
∑ |
379 |
231 |
25 |
|
x |
75.8 |
46.2 |
5 |
|
Var |
31.7 |
9.2 |
8.5 |
|
Arc sin = 58.693 |
Arc sin =42.130 |
Arc sin =9.974 |
|
Arc sin |
Arc sin = 45.000 |
Arc sin =15.341 |
|
Arc sin |
Arc sin 40.396 |
Arc sin = 11.536 |
|
Arc sin |
Arc sin =42.705 |
Arc sin =17.457 |
|
Arc sin |
Arc sin =42.853 |
Arc sin = 8.130 |
|
58.693 |
42.13 |
9.974 | |
|
56.166 |
56.166 |
15.341 | |
|
63.438 |
40.396 |
11.536 | |
|
65.649 |
42.705 |
17.457 | |
|
59.342 |
42.853 |
8.13 | |
|
∑ |
303.288 |
224.25 |
62.438 |
|
60.6576 |
44.85 |
12.4876 |
متولد 1362 کرمانشاه و مقیم تهران هستم تحصیلات مقاطع کاردانی، کارشناسی و کارشناسی ارشد را به ترتیب در دانشگاههای لرستان(تکنولوژی تولیدات دامی)، شهید با هنر کرمان(مهندسی تولیدات دامی)و کردستان(ژنتیک و اصلاح نژاد دام)گذرانده ام.