Regression-1 - xi*yi 1 2 3 4 5 6 7 0.5 2.5 2 4 3.5 6 5.5...

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xi*yi xi^2 (yi-ymean)^2 1 0.5 0.5 1 8.58 2 2.5 5 4 0.86 3 2 6 9 2.04 4 4 16 16 0.33 5 3.5 17.5 25 0.01 6 6 36 36 6.61 7 5.5 38.5 49 4.29 Sum(xi*yi)= 119.5 n= 7 Sum(xi^2)= 140 sqrt(Sr/(n-2))= a1= 0.84 a0= 0.07 xmean= 4 ymean= 3.43 S_t= 22.71 S_r= 2.99 S_t-S_r= 19.72 r^2= 0.87 0.84 0.07 a1 a0 0.15 0.65 s_a1 s_a0 0.87 0.77 r^2 Std Error 32.97 5 F stat Degr.of freedom 19.72 2.99 S_t-S_r S_r SUMMARY OUTPUT Regression Statistics Multiple R 0.93 R Square 0.87 Prevents r^2 to Adjusted R Squa 0.84 USED WHEN MORE THAN ONE X IS USED. Adj r^2= 1-(1-r^ Standard Error 0.77 Usually a population regression model is y = b1 + b2*x + Observations 7 u has ZERO mean, but a standard deviation… ANOVA Analysis of V df SS MS F Significance F MOST OF THE Regression 1 19.72 19.72 32.97 0 Residual 5 2.99 0.6 Total 6 22.71 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 0.07 0.65 0.11 0.92 -1.61 1.75 X Variable 1 0.84 0.15 5.74 0 0.46 1.22 All this is used to test hypothesis/ Coefficient=0 against no Column " P-value " 0 1 2
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