Practice Lab for Test 2 with Solution - Applied Regression Analysis | STAT 462, Exams of Statistics

Download Practice Lab for Test 2 with Solution - Applied Regression Analysis | STAT 462 and more Exams Statistics in PDF only on Docsity! 1 Practice Lab for Test #2 • Make sure you review the pure error lack of fit test, its requirements, the test statistic and its reference distribution under the null hypothesis. Also, make sure that you are familiar with the interpretation of the ANOVA output which includes the pure error decomposition, e.g.: • Make sure you can describe the implementation of the lowess smooth, and know how to use it in regression analysis. For instance, how would you interpret the following scatter plots with lowess smooth superimposed? (note the two plots concern different regression fits). 3025201510 90 80 70 60 50 40 30 20 10 0 x y Regress Lowess Fits 3025201510 3 2 1 0 -1 -2 -3 -4 x re si du al s Regress Lowess Fits • Review the use of predictor and response transformations as remedial measures. Analysis of Variance Source DF SS MS F P Regression 1 34644 34644 876.43 0.000 Residual Error 98 3874 40 Lack of Fit 19 1392 73 2.33 0.005 Pure Error 79 2482 31 Total 99 38518 2 • Compute the inverse of the matrix 2 4 3 1 A ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦ and verify that AA-1 = A-1A = I. • Let X indicate the design matrix of a simple linear regression. What are the formulae for each of the entries in the 2 by 2 matrix X’X? • Suppose you are given the following descriptive statistics for x: Compute the entries of X’X for this data, and then compute the inverse, (X’X)-1. • The variance/covariance matrix of intercept and slope estimates in a simple linear regression model can be obtained from the normal equations as follows: ' 'X X X Yβ = 10 1( , ) ' ( ' ) 'b b b X X X Y −= = 1 1cov( ) ( ' ) 'cov( )(( ' ) ') 'b X X X Y X X X− −= 1 2 1( ' ) '* * ( ' )X X X I X X Xσ− −= 2 1( ' )X Xσ −= where σ 2 is the error variance. Suppose that, in addition to the above descriptive statistics for x, you are also given the following regression output: Compute the entries of the estimated variance/covariance matrix. • Suppose you are given the following additional output: Variable N Mean StDev x 100 20.361 4.787 The regression equation: y = 4.79 + 1.01 x Predictor Coef SE Coef T P Constant 4.7927 0.4759 10.07 0.000 x 1.00902 0.02276 44.34 0.000 S = 1.08398 R-Sq = 95.3% New x Fit SE Fit 90% CI 15 19.928 0.163 (19.657, 20.199) x Fit SE Fit 90% CI 25 30.018 0.151 (29.767, 30.269) Student's t distribution with 98 DF P( X <= x ) x 0.9 1.29025 P( X <= x ) x 0.95 1.66055 P( X <= x ) x 0.975 1.98447