mont4e_sm_ch11_supplemental

mont4e_sm_ch11_supplemental - 11-49Supplemental...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 11-49Supplemental Exercises11-78 a) ∑∑∑===−=−niiniiniiiyyyy111ˆ)ˆ(and ∑∑+=iixny1ˆˆββfrom the normal equations Then, ˆˆˆˆ)ˆˆ(ˆˆˆ)ˆˆ(1111111111=−−+=+−+=−+∑∑∑∑∑∑=====niiniiniiniiiniixnxnxxnyxnββββββββββb) iniiiniiiniiixyxyxyy∑∑∑===−=−111ˆ)ˆ(and ∑∑∑===+=niiniiiniixxxy12111ˆˆββfrom the normal equations. Then, ˆˆˆˆ)ˆˆ(ˆˆ12111211111211=−−+=+−+∑∑∑∑∑∑∑=======niiniiniiniiiininiiniixxxxxxxxββββββββc) yynnii=∑=1ˆ1)ˆˆ(ˆ1xyββ∑∑+=yxxyxxnynnxxynnxnnxnyniiiinii=+−=+−=+−=+=+=∑∑∑∑∑=11111111ˆˆ)ˆˆ(1)ˆ)ˆ((1)ˆˆ(1)ˆˆ(1ˆ1ββββββββββ11-5011-79 a) 1.11.31.51.71.92.1x0.711.31.61.92.2yPlot of y vs xYes, a linear relationship seems plausible. b) Model fitting results for: y Independent variable coefficient std. error t-value sig.level CONSTANT -0.966824 0.004845 -199.5413 0.0000 x 1.543758 0.003074 502.2588 0.0000 -------------------------------------------------------------------------------- R-SQ. (ADJ.) = 1.0000 SE= 0.002792 MAE= 0.002063 DurbWat= 2.843 Previously: 0.0000 0.000000 0.000000 0.000 10 observations fitted, forecast(s) computed for 0 missing val. of dep. var. ¡..yx= −+0 966824 154376c) Analysis of Variance for the Full Regression Source Sum of Squares DF Mean Square F-Ratio P-value Model 1.96613 1 1.96613 252264. .0000 Error 0.0000623515 8 0.00000779394 -------------------------------------------------------------------------------- Total (Corr.) 1.96619 9 R-squared = 0.999968 Stnd. error of est. = 2.79176E-3 R-squared (Adj. for d.f.) = 0.999964 Durbin-Watson statistic = 2.84309 2) H1:β=3) H11:β≠4) α= 0.05 5) The test statistic is )/(/pnSSkSSfER−=6) Reject Hif f> fα,1,8where f0.05,1,8= 5.32 7) Using the results from the ANOVA table 9.2552638/0000623515.1/96613.1==f8) Because 2552639 > 5.32 reject Hand conclude that the regression model is significant at α= 0.05. P-value < 0.000001 d) 95 percent confidence intervals for coefficient estimates -------------------------------------------------------------------------------- Estimate Standard error Lower Limit Upper Limit CONSTANT -0.96682 0.00485 -0.97800 -0.95565 x 1.54376 0.00307 1.53667 1.55085 -------------------------------------------------------------------------------- 11.536671.55085β≤≤e) 2) H:β=11-513) H1:β≠4) α= 0.05 5) The test statistic is tse=¡(¡)ββ6) Reject Hif t< −tα/2,n-2where −t0.025,8= −2.306 or t> t0.025,8= 2.306 7) Using the results from the table above t0 966820 00485199 34=−= −....
View Full Document

This note was uploaded on 10/12/2009 for the course IND E 315 taught by Professor Kailashkapur during the Spring '09 term at University of Washington.

Page1 / 10

mont4e_sm_ch11_supplemental - 11-49Supplemental...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online