The viscosity () of an ol was measured by a cone and plate viscometer at seven d
ID: 3045903 • Letter: T
Question
The viscosity () of an ol was measured by a cone and plate viscometer at seven different cone speeds (x). It was assumed that a quadratic regression model was appropriate, and the estimated regression function resulting from the n = 7 observations was y =-113.0937 + 3.3684x-0.01780x (a) Estimate -72, the expected viscosity when speed is 72 rpm. (Round your answer to two decimal places.) (b) What viscosity would you predict for a cone speed of 63 rpm? (Round your answer to two decimal places.) (c) lfSy 2-8381.43,= 210.40, ,-17,002, and 2y; = 1,419,790, compute SSE = 2-PoSy-AExiyi-2Ex?y; and s. (Round your answers to two decimal places.) SSE s= (d) From part (c), SST 8381.43 (210.40)2/7 2057.41. Using SSE computed in part (c), what is the computed value of R? (Round your answer to three decimal places.) (e) If the estimated standard deviation of 2 is si2-0.00222, test H0 2 0 versus H 2 # 0 at level 001, and interpret the result. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) P-value = State the conclusion in the problem context. Fail to reject Ho. The quadratic term is not statistically significant in this model. Fail to reject Ho. The quadratic term is statistically significant in this model Reject Ho. The quadratic term is not statistically significant in this model Reject Ho. The quadratic term is statistically significant in this model.Explanation / Answer
a)
when x = 72
= -113.0937 + 3.3684*72-0.0178*72^2
=37.1559
b)
x = 63
y^ = 28.4673
c)
SSE = =8381.43-(-113.0937*210.4)-3.3684*17002+0.0178*1419780
= 178.8917
s = sqrt(SSE/(n-k-1)) = sqrt(178.8917/(7-2-1))
= 6.68752
d)
R^2 = 1- SSE/SST = 1 - 178.8917/2057.41
= 0.91305
e)
t = -0.0178/0.00222 = -8.01802
p-value= 0.0000
option D) rejec Ho, the quadratic term is statistically significant
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