Question

I figured the number 380.25 should related to quadratic model. is it correct> if it is, how did he get this number tho. if not, how did he get the number

Thanks

Problem For Exercise 12.8 on page 451, construct a 90%_cenidence inteaval for the mean compressive strength when the concentration is x = 19.5 and a adratic model used 12.8 The following is a set of coded experimental cata on the compressive strength of a particular alloy at var- ious values of the concentration of some additive: Concentration, Compressive Strength, y 25.2 29.8 31.2 31.7 29.4 27.3 31.1 32.6 30.1 28.7 27.8 29.7 32.3 10.0 15.0 20.0 25,0 30.0 30.8 32.8 (a) Estimate the quadratic regression equation Ayr = Bo+B1 B2r2. (b) Test for lack of fit of the model. Step-by-step solution Step 1 of 5A We know that a 100(1-a) % confidence interval for the predicted mean response is -u/+x(xx)x,<y, < ?,+Sq/l+ x6(x'x) x . where uis is a value of the t-distribution with n-k-1 degrees of freedom. x is often called the standard error of prediction. The quantity xX'X Comment Step 2 of 5 A For the given problem we have n 15 and k 2. After fitting a quadratic regression model we have y19.01.01 x - 0.0204 x The predicted value of the response variable y when x 19.5 is y = 19,01,01 x -0.0204 x 19.01.01 (19.5) - 0.0204 (19.5) 30.9379

Answer 1

Yes, the number 380.25 is correct. xo' is actually the following matrix:

x₀' = [x⁰ x¹ x²] = [19.5⁰ 19.5¹ 19.5²]

As x = 19.5, for the quadratic model:

x₀' = [1 19.5 380.25]