Question

9 (y - y)(y - )? (9 - 7) 100 100 100 100 200 200 200 200 500 500 500 500 16.7 12.2 8.4 6.6 15.3 10.71 10.3 21.1 45.6 43.9 47.7 43.2 SSE SST SSR 3. Complete all remaining columns of the table above using the regression equation you found and then find the sum of squared values (SSE, SST and SSR). Complete the given ANOVA table and comment whether the regression coefficient related to the factor's main effect is statistically significant. Use a significance level of 0.05. Sum of Squares Source of Error DOF Mean Squares Fvalue p-value Model SSR= Ebi - ) a-1 MSR MSR MSE SSR dfr SSE dfe From Ftable Error n-a MSE SSE = (yi - 9:) SST = lyi- y) Total n-1 ΑΛΑΤΙΑ

Answer 1

for x =100

$\small \hat y =\frac{16.7+12.2+8.4+6.6}{4}=10.975$

for x =200

$\small \hat y =\frac{15.3+10.7+10.3+21.1}{4}=14.35$

for x =500

$\small \hat y =\frac{45.6+43.9+47.7+43.2}{4}=45.1$

x	y
100	16.7
100	12.2
100	8.4
100	6.6
200	15.3
200	10.7
200	10.3
200	21.1
500	45.6
500	43.9
500	47.7
500	43.2
Total	281.7
Avearge	23.475

So,

$\bar y= 23.475$

Subsituting value in table so,

x	y	$\hat y$	$(y-\hat y)^2$	$(y-\bar y)^2$	$(\hat y-\bar y)^2$
100.00	16.70	10.98	32.78	45.90	156.25
100.00	12.20	10.98	1.50	127.13	156.25
100.00	8.40	10.98	6.63	227.26	156.25
100.00	6.60	10.98	19.14	284.77	156.25
200.00	15.30	14.35	0.90	66.83	83.27
200.00	10.70	14.35	13.32	163.20	83.27
200.00	10.30	14.35	16.40	173.58	83.27
200.00	21.10	14.35	45.56	5.64	83.27
500.00	45.60	45.10	0.25	489.52	467.64
500.00	43.90	45.10	1.44	417.18	467.64
500.00	47.70	45.10	6.76	586.85	467.64
500.00	43.20	45.10	3.61	389.08	467.64
Total	281.70		148.30	2976.92	2828.63

So,

SSR	2828.63
SSE	148.30
SST	2976.92

as given

a=3

n=12 so

	DOF
Model	2.00
Error	9.00
Total	11.00

now subsituting all value in anova table

Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value C1 2 2828.6 1414.31 85.83 0.000 Error 9 148.3 16.48 Total 11 2976.9

For α=0.05

$\\\\F_{\alpha,a-1,n-a}=F_{0.05,2,9}=4.26 \\\\F_o(\text{From ANOVA table})=85.83 \\\\\text{we reject null Hypothesis since }F_o>F_{0.05,2,9}$

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