80. The article Analysis of the Modeling Methodologies for Predicting the Strength of Air-Jet Spun Yarns (Textile Res. J., 1997: 39—44) reported on a study carried out to relate yarn tenacity (y, in g/tex)

to yarn count (x1, in tex), percentage polyester (x2), rst 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 6.121. The estimated coef cients for the four predictors were .082, .113, .256, and

.219, respectively, and the coef cient of multiple determination was .946. Assume that n  25.

a. State and test the appropriate hypotheses to decide whether the tted model speci es a useful linear relationship between the dependent variable and at least one of the four model predictors.

b. Calculate the value of adjusted R2 and comment.

c. Calculate a 99% con dence interval for true mean yarn tenacity when yarn count is 16.5, yarn contains 50% polyester, rst nozzle pressure is 3, and second nozzle pressure is 5 if the estimated standard deviation of predicted tenacity under these circumstances is .350.