An experiment was conducted to investigate the effects of a new technique for de

Question

An experiment was conducted to investigate the effects of a new technique for degumming of silk yarn. One response variable of interest was y = weight loss %). The experimenters made observations on weight loss for various values of three independent variables: x1 = temperature °C -90 100 110; X2-time of treatment min)-30, 75 120; X3-tartaric acid concentration g/L -0, 8 16 In the regression analyses, the three values of each variable were coded-,0, and 1, respectively, giving the accompanying data. obs 4 5 9 10 11 12 13 1413 -1 1 1 -1-1 1 1000 0 *3 0 0 -1 1 -1 1 1 -1100 0 18.5 22.7 22.6 22.8 3.8 19.3 19.5 20.3 13.0 23.1 21.4 21.4 22.1 20.9 22.5 A multiple regression model with k 9 predictor X1, x2, x3: x.-x12 5-r22.*6 x32 x,-X1X2, xs-r1 3, x#x2x3 was fit to the data, resulting in .-21.833, .-2.613, 2 5 = 1.908, 5 = 4.017, 7 = -1.000, 8 =3.675, 9 = 2.525, 55E = 26.384, and R2 = 0.926, 1.388, 31 3.300, .--2092 (a) Does this model specify a useful relationship? State and test the appropriate hypotheses using a significance level of 0.01 State the appropriate hypotheses. Hai no ,-0 Ha: at least one : 0 Ha: at least one Ha: all A's = 0 Calculate the test statistic. (Round your answer to two decimal places.)

Explanation / Answer

The statistical softwre output for this problem is:

Multiple linear regression results:
Dependent Variable: y
Independent Variable(s): x1, x2, x3
y = 19.593333 + 2.6125 x1 + 1.3875 x2 + 3.3 x3

Parameter estimates:

Analysis of variance table for multiple regression model:

Summary of fit:
Root MSE: 4.2832319
R-squared: 0.4378
R-squared (adjusted): 0.2844

Hence,

Test statistic:

f = 2.85

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 19.593333 1.1059257 0 11 17.716681 <0.0001 x1 2.6125 1.5143512 0 11 1.7251613 0.1124 x2 1.3875 1.5143512 0 11 0.91623398 0.3792 x3 3.3 1.5143512 0 11 2.1791511 0.0519

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