A study was carried out to relate yarn tenacity (y, in g/tex) to yarn count (x1, in tex), percentage polyester (x2), first nozzle pressure (x3, in kg/cm2), and second nozzle pressure (x4, in kg/cm2). The estimate of the constant term in the corresponding multiple regression equation was 6.122. The estimated coefficients for the four predictors were 0.081, 0.111, 0.259, and 0.216, respectively, and the coefficient of multiple determination was 0.951. (a) Assuming that the sample size was n = 25, state and test the appropriate hypotheses to decide whether the fitted model specifies a useful linear relationship between the dependent variable and at least one of the four model predictors. (Use alpha = 0.001).
1. State the appropriate hypotheses.(4 choices)
A. H0: ?1 ? ?2 ? ?3 ? ?4 ? 0
Ha: at least one among ?1, ..., ?4 is zero
B. H0: ?1 = ?2 = ?3 = ?4 = 0
Ha: at least one among ?1, ..., ?4 is not zero
C. H0: ?1 = ?2 = ?3 = ?4 = 0
Ha: no ?i = 0
D. H0: ?1 ? ?2 ? ?3 ? ?4 ? 0
Ha: ?1 = ?2 = ?3 = ?4 = 0
2. State the rejection region and compute the test statistic value.
3. State the conclusion in the problem context.
A. Reject H0. The model is judged useful.
B. Fail to reject H0. The model is judged useful.
C. Fail to reject H0. The model is judged not useful.
D. Reject H0. The model is judged not useful.
(b) Again using n = 25, calculate the value of adjusted R2.
(c) Calculate a 99% confidence interval for true mean yarn tenacity when yarn count is 16.1, yarn contains 50% polyester, first nozzle pressure is 3, and second nozzle pressure is 5 if the estimated standard deviation of predicted tenacity under these circumstances is 0.35.