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STAT3038 assignment

by: Guoshen Zheng

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5

STAT3038 assignment

Marketplace > University of Cincinnati > > STAT3038 assignment
Guoshen Zheng
UC

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This 5 page Class Notes was uploaded by Guoshen Zheng on Friday March 25, 2016. The Class Notes belongs to at University of Cincinnati taught by in Summer 2015. Since its upload, it has received 33 views.

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Date Created: 03/25/16
Surname 1 Name: Tutor: Course: Date:  a) Fitting a regression model y=348.8458−1.30386x1−0.15122x2 Where y is the wear, x1 the oil viscosity and x2 the load. b) Under the assumption that the error term has a constant variance, then the estimate of the  variance is given by 2 SSE σ = n−2 2 1919.244 σ = 3 =639.748 c) ANOVA   D f SS MS F Significance F Regression 2 12192.76 6096.378 9.529345 0.050155 Residual 3 1919.244 639.7479 Total 5 14112       d) Surname 2 95% CI for the intercept coefficient 95%CI for bo=bo±z∗SEbo 95%CI for bo=348.8458±1.96∗74.7855 ¿(202.266,495.425) 95% CI for the oil viscosity coefficient 95%CI for bo=bo±z∗SEbo 95%CI for bo=−1.3039±1.96∗1.1654 ¿(−3.5881,0.9803) 95% CI for the load coefficient 95%CI for bo=bo±z∗SEbo 95%CI for bo=−0.1512±1.96∗0.08962 ¿(−0.3269,0.0245) e) 90% CI for the mean wear 90%CI for meanwear=bo±z∗MSE 90%CI forbo=348.8458±2.58∗639.7479 ¿(−1301.7038,1999.395) Surname 3 90% prediction interval for the observed wear at x1=20 and x2=1000 y=348.8458−1.30386x1−0.15122x2 y=348.8458−1.30386(20)−0.15122(1000) y=171.5486 90%CI forobserved wear=observed ±z∗MSE 90%CI forbo=171.5486±2.58∗639.7479 ¿(−1479.0,1822.098) f) Test of hypothesis H0: β1 = 0 versus H1: β1 ≠ 0 b1 t= Sb1 −1.303858 t= =−1.11877 1.16544 The probability value associated with this t­statistic is 0.34474>0.05. Since the p­value was  greater than the alpha value, the null hypothesis was not rejected. Hence, β1 = 0. H0: β2 =0 versus H1: β2 ≠ 0 b2 t=Sb2 Surname 4 −0.1512 t= 0.08962 =−1.6873 The probability value associated with this t­statistic is 0.1901>0.05. Since the p­value was  greater than the alpha value, the null hypothesis was not rejected. Hence, β2 = 0. h) The model M1 should be changed. This is because the two independent variables were not  effective as indicated by the significance of b1 and b2.  i) Model 1 (M1) main effects Regression Statistics Multiple R 0.929516 R Square 0.863999 Adjusted R Square 0.773332 Standard Error 25.29324 Observations 6 Model 2 (M2) with interactions Regression Statistics Multiple R 0.959201 R Square 0.920067 Adjusted R Square 0.800167 Standard Error 23.74886 Observations 6 Model 3 (M3) with interaction term and quadratic terms Regression Statistics Multiple R 1 R Square 1 Adjusted R Square 65535 Surname 5 Standard Error 0 Observations 6 The values for the R­square are 0.863999, 0.920067 and 1 for the M1, M2 and M3  respectively. The adjusted R­square are 0.773332, 0.800167 and 65535 for the M1, M2 and  M3 respectively It is clear that model 2 is better than model 1 while model 3 is the best.

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