tut1_09 - Department of Statistical and Actuarial Sciences...

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Unformatted text preview: Department of Statistical and Actuarial Sciences Statistical Sciences 3859 Tutorial 1 1. 25 observations were taken on the electrical output of a windmill generator. Each observation consists of a measurement x , representing the wind velocity, and a measurement y , representing the DC electrical output. Some sample statistics on these data show: ∑ x i = 153 . 3, ∑ y i = 40 . 2, ∑ x 2 i = 1094, ∑ y 2 i = 75, and ∑ x i y i = 284. (a) Find estimates of the slope and intercept parameters in a linear regression of y on x . (b) Estimate the error variance using an unbiased estimator. (c) Estimate the standard error of the slope estimate. (d) Obtain the ANOVA table, and use it test whether the slope differs from 0, using a 5% level. (e) Compute the sample correlation coefficient between y and x . (f) Calculate the coefficient of determination. (g) What percentage of the total variability in y is explained by the model?...
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