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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Unformatted text preview: xi*yi 1 2 3 4 5 6 7 0.5 2.5 2 4 3.5 6 5.5 Sum(xi*yi)= 7 n= xi^2 0.5 5 6 16 17.5 36 38.5 119.5 Sum(xi^2)= (yi-ymean)^2 8.58 0.86 2.04 0.33 0.01 6.61 4.29 1 4 9 16 25 36 49 140 sqrt(Sr/(n-2))= a1= a0= xmean= 0.84 0.07 4 ymean= 0.84 0.15 0.87 32.97 19.72 3.43 S_t= 0.07 a1 0.65 s_a1 0.77 r^2 5 F stat 2.99 S_t-S_r 22.71 S_r= S_t-S_r= a0 s_a0 Std Error Degr.of freedom S_r 2.99 19.72 r^2= 0.87 7 6 5 4 3 2 1 0 SUMMARY OUTPUT 0 1 2 3 4 Regression Statistics Multiple R 0.93 R Square 0.87 Prevents r^2 to grow indefinitely Adjusted R Square 0.84 USED WHEN MORE THAN ONE X IS USED. Adj r^2= 1-(1-r^2)*(n-1)/(n-k-1) Standard Error 0.77 Usually a population regression model is y = b1 + b2*x + u Observations 7 u has ZERO mean, but a standard deviation… ANOVA df Regression Residual Total Intercept X Variable 1 SS MS 1 5 6 19.72 2.99 22.71 Coefficients 0.07 0.84 Standard Error 0.65 0.15 19.72 0.6 t Stat Analysis of Variance. F Significance F MOST OF THE TIME THIS IS IG 32.97 0 P-value Lower 95% Upper 95% 0.11 0.92 -1.61 1.75 5.74 0 0.46 1.22 All this is used to test hypothesis/ Coefficient=0 against not equal zero. Column "P-value" is the Pr{|t| > t-Stat}where t is a t-distributed random variable with n-k degree computed value of the t-statistic given in the previous column. Note that this p-value is for a two-sided test. For a one-sided test divide this p-value by 2 (also checking the sign of the t-S Columns "Lower 95%" and "Upper 95%" values define a 95% confidence int (yi-y_line)^2 0.17 0.56 0.35 0.33 0.59 0.8 0.2 0.77 sqrt(Sr/n)= 0.65 http://office.microsoft.com/en-us/assistance/HA011119631033.aspx 2 3 4 5 6 7 8 vents r^2 to grow indefinitely by adding indep. Variables j r^2= 1-(1-r^2)*(n-1)/(n-k-1) (1-Adj r^2)= (1-r^2)*(n-1)/(n-k-1) b1 + b2*x + u alysis of Variance. OST OF THE TIME THIS IS IGNORED Lower 95.0%Upper 95.0% -1.61 1.75 0.46 1.22 0 against not equal zero. ndom variable with n-k degrees of freedom and t-Stat is the revious column. lso checking the sign of the t-Stat). s define a 95% confidence interval for b2. ...
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This note was uploaded on 08/31/2011 for the course ENGR 3723 taught by Professor Staff during the Summer '11 term at Oklahoma State.

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