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(i) Test for the existence of regression (the F-test). Carefully de ne the null and alternative hypothesis, and explain the result of any R output you obtain.
(ii) Which of the 12 explanatory variables are not signi cantly associated with quality given that the other 11 variables are included in the model?
(iii) Fit the model using the 11 covariates that are signi cantly associated with quality. Calculate the R2 and adjusted-R2 value for your new model, and for the full model that used all 12 covariates. You should have found that R2 decreases upon removal of the unnecessary covariate, but that the adjusted-R2 increased. Explain this nding.
(iv) Carry out a partial F test to decide if inclusion of log(pH) provides a signi cant improvement over the model that just uses the 11 covariates. Repeat this analysis to decide whether adding (density) provides a signi cant improvement. Be sure to carefully de ne the null and alternative hypothesis and the procedure you use to do the test.
There are many situations which call for the replacement of an integral by a sum, or vice versa. In the former case the highest accuracy is sometimes required. This means that in t
Code and test Jacobi and Gauss-Sidel solvers for arbitrary diagonally dominant linear systems.
WHY IS SINp = 0
prove that A=3i+j-2k ,B= -i+3j+4k, C=4i-2j-6k can form a triangle and find the length of the medians of the triangle.
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1. Joe and Sam each invested $20,000 in the stock market. Joe's investment increased in value by 5% per year for 10 years. Sam's investment decreased in value by 5% for 5 years and
for what values of (a,b) does the point P (0,a,b) lie on the line through Q (1,-1,4) and R (2,3,5)?
A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i
Draw concentric circles of radii a and b, each centered at z=id (on the imaginary axis). Suppose φ(x,y) is a harmonic function inside the washer defined by these circles. The circl
A manager has determined the cost C, in dollars, for manufacturing is C(q) =85log 10 (10+q/2) for manufacturing, where q is the number of units produced in a given day. (a
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