1 answer

Please show all work. Thank you in advance! :) 4.14. The survival rate (in percentage) of bull semen after storage

Question:

4.14. The survival rate (in percentage) of bull semen after storage is measured at various combinations of concentrations of

% Survival % Weight 1 % Weight 2 % Weight 3 (x2) (xi) (x3) 4.10 6.62 26.4 8.00 6.32 25.9 32.0 9.10 8.72 4.42 4.08 8.70 7.60 4

d. Construct a 90% confidence interval for i. the predicted mean value of y when Xi-3, X2-8, and X3-9; ii. the predicted indi

Please show all work. Thank you in advance! :)

4.14. The survival rate (in percentage) of bull semen after storage is measured at various combinations of concentrations of three materials (additives) that are thought to increase the chance of survival. The data listed below are given in the file bsemen % Survival % Weight 1 % Weight 2 % Weight 3 (x3) (x2) (xi) 1.74 6.32 25.5 5.30 10.80 31.2 5.42 9.40 8.41 4.63 11.60 6.22 25.9 7.20 38.4 10.52 8.50 1.19 1.22 18.4 9.40 26.7 9.90 5.85
% Survival % Weight 1 % Weight 2 % Weight 3 (x2) (xi) (x3) 4.10 6.62 26.4 8.00 6.32 25.9 32.0 9.10 8.72 4.42 4.08 8.70 7.60 4.83 4.15 25.2 9.20 10.15 1.72 39.7 9.40 3.12 35.9 7.60 26.5 1.70 5.30 8.20 Assume the model y = At Axi + Ax2 +
d. Construct a 90% confidence interval for i. the predicted mean value of y when Xi-3, X2-8, and X3-9; ii. the predicted individual value of y when Xi-3, X2-8, and X3-9 e. Construct the ANOVA table and test for a significant linear relationship between y and the three predictor variables.

Answers

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.95357488
R Square 0.909305052
Adjusted R Square 0.879073403
Standard Error 2.107691293
Observations 13
ANOVA
df SS MS F Significance F
Regression 3 400.8510444 133.617 30.07792 5.07165E-05
Residual 9 39.98126328 4.442363
Total 12 440.8323077
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 39.48151839 5.985544416 6.596145 9.97E-05 25.94127621 53.02176056
X Variable 1 1.0092246 0.194088687 5.199812 0.000564 0.570165487 1.448283714
X Variable 2 -1.87265715 0.271797595 -6.8899 7.15E-05 -2.487506028 -1.257808277
X Variable 3 -0.36669973 0.62737472 -0.5845 0.573243 -1.785919946 1.052520486

d. У-39.48 15 + 1.0092x1-1.8727T2-0.3667x3. where, βι = 1.0092, standard error of β1 = se(A) = 0.1941; B2 =-1.8727, standard

(ii) 90% P.I. for the y when x1-3, x2-8, x3-9 is 90% С.Г. for the predicted mean value oy y when x1-3, x2-8, x3-9 is MSE3 MSE

e.

ANOVA
df SS MS F Significance F
Regression 3 400.8510444 133.617 30.07792 5.07165E-05
Residual 9 39.98126328 4.442363
Total 12 440.8323077

Since p-value<0.05 so we conclude that linear relationship between y and the three predictors is significant.

.

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