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HW3sol

# HW3sol - 1 KNNL Problem 2.26 To change the axis on a plot...

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1. KNNL Problem 2.26. To change the axis on a plot, add an “order” statement to the axis definition. For example, to make the vertical axis go from -30 to 30 in increments of 10, do axis3 label=(angle=90 ‘Residuals’) order=(-30 to 30 by 10); Then use vaxis=axis3 as an option to the plot statement, along with haxis and vref=0. The mean value of Y appears as Dependent Mean in the output from proc reg. 2.26: Refer to Plastic hardness Problem 1.22. (a) Set up the ANOVA table. Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 5297.51250 5297.51250 506.51 <.0001 Error 14 146.42500 10.45893 Corrected Total 15 5443.93750 (b) Test by means of an F test whether or not there is a linear association between the hardness of the plastic and the elapsed time. Use a = .01. State the alternatives, decision rule, and conclusion. Testing H 0 : β 1 = 0 vs H a : β 1 0. Reject H 0 if P-value < 0.01. Since P-value < 0.0001, we reject H 0 and conclude that there is a significant linear relationship between hardness and time. (c) Plot the deviations ˆ i i Y Y - against X i on a graph. Plot the deviations ˆ i Y Y - against X i on another graph, using the same scales as for the first graph. From your two graphs, does SSE or SSR (SSM) appear to be the larger component of SSTO (SST)? What does this imply about the magnitude of r 2 ?

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R e s i d u a l s ( O b s e r v e d - P r e d i c t e d ) - 3 0 - 2 0 - 1 0 0 1 0 2 0 3 0 t i me ( h o u r s ) 1 0 2 0 3 0 4 0 D e v i a t i o n s ( P r e d i c t e d - Me a n ) - 3 0 - 2 0 - 1 0 0 1 0 2 0 3 0 t i me ( h o u r s ) 1 0 2 0 3 0 4 0 On the graphs, it is apparent that the residuals ˆ i i Y Y - are much smaller than the deviations ˆ i Y Y - of the predictors from the mean. Thus the SSM should be much larger than the SSE, and we expect 2 SSM r SST = to be close to 1.
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HW3sol - 1 KNNL Problem 2.26 To change the axis on a plot...

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