# UFFI_hyptest_and_CI.pdf - UFFI example hypothesis tests and...

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UFFI example- hypothesis tests and confidence intervalsLet’s check our hand calculations of the UFFI dataset from chapter 1, p.7.Hypothesis testsetwd("~/Documents/Stat 353/2007")uffi=read.table("uffi.txt",header=T)attach(uffi)fit=lm(CH2O~Air+UFFI)summary(fit)#### Call:## lm(formula = CH2O ~ Air + UFFI)#### Residuals:##Min1QMedian3QMax## -9.5460 -3.1312 -0.13893.57798.3620#### Coefficients:##Estimate Std. Error t value Pr(>|t|)## (Intercept)31.37342.460712.750 2.36e-11 ***## Air2.85450.37647.584 1.92e-07 ***## UFFI9.31202.13254.3670.00027 ***## ---## Signif. codes:0***0.001**0.01*0.05.0.11#### Residual standard error: 5.223 on 21 degrees of freedom## Multiple R-squared:0.7827, Adjusted R-squared:0.762## F-statistic: 37.82 on 2 and 21 DF,p-value: 1.095e-07Check thatˆβUF F I= 9.312, SE(ˆβUF F I)=2.1325Notice also that “Residual standard error”=s, thuss2= 5.2232= 27.28. Notice also in the ANOVA below,MSE=27.28.What does the t-value represent? This is the test statistics associated with