**IF given a FINITE population and n/N > 5% apply the “Finite Correction Factor”Compute the Z-score and use =NORMSDIST(z) (π = Population %, p = sample %)SUMMARY OUTPUTRegression StatisticsMultiple R r = sqrt(R Square) ranges from -1 to 1. Indicates direction and strength of the relationship between variablesR Square R² = SSR/SST ranges from 0 to 1. Indicates % of variation in predicted value that is influenced by the variation in x-variablesAdjusted R Square =1-[(1-R²)(n-1)/(n-k-1)]adjusted for number of explanatory/independent variables (x-variables)Standard Error =sqrt(MSE) Standard Error for the predicted valueObservations n = df_total + 1ANOVAdf SS MS F Significance FRegression k = # of x-variables SSR = ∑(ŷ- )²ȳ MSR = SSR/k F Test Stat = MSR/MSEP-value for F Test (see below)Residual df = n - k - 1 SSE = ∑(y-ŷ)² MSE = SSE/df(variance)Total Total = k + df SST = ∑(y- )²ȳCoefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept y-int =tstat*se se =coeff/tstat t stat = coeff/se =Prob beyond t Stat =coeff - CV*(stderror) =coeff + CV*(stderror)BOOKS slope X1 =tstat*se = (slope-0)/se slope X1 - ME slope X1 + MEATTEND slope X2 =tstat*se = r*(sqrt((n-2)/(1-R²)) 'slope X2 - ME 'slope X2 + MESample Statistic PopulationParameterr ρR² ρ²b βNull Hypothesis AlternativeHypothesisFound in output Type and Nature ofTestCritical Value(s) P-ValueH0: β1 =β2 = 0 H1: At least one βi ≠ 0ANOVA Right Tailed F test=F.INV.RT(alpha,k,df)=F.DIST.RT(Fteststat,k,df)H0: ρ² ≤ 0 H1: ρ² > 0 ANOVA Right Tailed F testH0: βi = 0 H1: βi ≠ 0 Individ.Coefficients2 Tailed T Test= T.INV.2T(alpha,df)=T.DIST.2T(Tteststat*,df)*Tteststat > 0H0: ρ ≤ 0 H1: ρ > 0 Individ.Coefficients2 Tailed T Test EXCEL FORMULA SHEET DISTRIBTIONS Binomial Distributions For an EXACT probability :=BINOMDIST(x,n,p,false) For less than or equal to x (at most x): =BINOMDIST(x, n, p, true) For less than x : =BINOMDIST((x-1), n, p, true)For greater than x : =1-BINOMDIST(x, n, p, true) For greater than or equal to x (at least x) : =1-BINOMDIST((x-1), n, p, true) Normal Distributions =NORMSDIST(z) p(z<?) =1-NORMSDIST(z) p(z>?) =NORMSDIST(z1) – NORMSDIST(z2) (used for “between” probabilities) For an EXACT probability *You will not be given “exact” probabilities because these are continuous distributions and exact values cannot be measured. For probability less than or equal to x (at most x) : =NORMDIST(x, mean, stddev, true) For probability less than x : *same as above since Normal Distributions are continuous! For probability greater than x : =1-NORMDIST(x,mean, stddev, true) For probability greater than or equal to x (at least x) : *same as above since Normal Distributions are continuous! Given the percentile (probability) with objective to find the data value (x-value) : =NORMINV(percentile, mean, stddev) If SAMPLING….with intent to determine the probability of the AVERAGE (mean) of the SAMPLE =NORMDIST(sample MEAN, population MEAN, STDERROR, true) *where STDERROR of the MEAN is: **IF given a FINITE population and n/N > 5% apply the “Finite Correction Factor” IF computing the STDERROR of a PROPORTION instead of the Mean: Compute the Z-score and use =NORMSDIST(z) (π = Population %, p = sample %)Critical Values=NORM.S.INV(alpha) (if left tailed negate the CV)(if two-tailed enter half of alpha)=T.INV(alpha,df)(if left tailed negate the CV)=T.INV.2T(alpha,df)(enter alpha, NOT half alpha)p-value:=NORM.S.DIST(teststat,true) (if right tailed subtract from 1)(if 2 tailed, double area in 1 tail)=T.DIST(teststat,df,true)=T.DIST.RT(teststat,df)=T.DIST.2T(teststat,df)(teststat MUST be positive)=CONFIDENCE (alpha, standard_dev,