\(SSE=\sum_{i=1}^{n}|\hat{Y}_{i}-b_0|\)
\(SSE_A=(\sum_{i=1}^{n}|Y_{i}-b_0|)^2*n-1\) only when it is a simple model aka when MSE=variance and RMSE is standard deviation
so: \(SSE_A=SD*n-1\)
with SSE
\(SSR= SSE_C - SSE_A\)
with data points aka STARBURST
\(SSR=\sum_{i=1}^{n}(\hat{Y}_{iC}-\hat{Y}_{iA})^2\)
\(SSR=n(\hat{Y}_{iC}-\hat{Y}_{iA})^2\)
with SSE
\(MSE= \frac{\sum|\hat{Y}_{i}-b_0|} {n-P_A}\)
or
\(MSE= \frac{SSE} {df}\)
in the simple model MSE= variance!!!
\(RMSE=\sqrt(MSE)\)
**in a simple model, MSE= variance (\(S^2\)), RMSE= standard deviation (s)
with SSE
\(PRE=\frac{ SSE_C - SSE_A} {SSE_C}\)
with SSR
\(PRE=\frac{SSR} {SSE_C}\)
with PRE
\(F_{(P_a-P_c, n-P_a)}=\frac{\frac{PRE}{P_a-P_c}}{\frac{1-PRE}{n-P_a}}\)
with SSE
\(F_{(P_a-P_c, n-P_a)}=\frac{\frac{SSR}{P_a-P_c}}{\frac{SSE_a}{n-P_a}}\)
with MS
\(F_{(P_a-P_c, n-P_a)}=\frac{MSR} {MSE}\)
with mean and null
\(t_{(n-1)}=\frac{\overline{Y}-B_o} {\frac{S_Y}{\sqrt(n)}}\)
with F
\(t_{(n-1)}=\sqrt(F*)\)
with F and MSE
\({b_{0}}\:\pm \sqrt{(F_{crit;1,n-P_A;\alpha} \: * \: (MSE))/n}\)
with PRE and \(SSE_C\)
\({b_{0}}\:\pm \sqrt{(PRE_{crit;1,n-P_A;\alpha} \: * \: (SSE_C))/n}\)
with T crit
\({b_{0}}\:\pm T_{crit;1,n-P_A;\alpha} \: * \: \frac{RMSE}{\sqrt{n}}\)
\({b_{0}}\:\pm T_{crit;1,n-P_A;\alpha} \: * \: \frac{SD}{\sqrt{n}}\)
\(1- ((1-PRE)*\frac{n-P_C} {n-P_A})\)
\(f2= \eta^2/(1-\eta^2)\)