John and Mary are social scientists. They collected replicated data of the form

Question

John and Mary are social scientists. They collected replicated data of the form (zi, Yu), i 1,...,k, j 1, m. John plotted Yi. 1 Yy/m vs r, and claimed that there is a nonlinear relationship between the response variable Y and the explanatory variable r, Mary used ordinary least squares to fit a linear model Yu Bi B2r, cu and claimed that a straight line model was adequate to fit the data because she found R2 0.9. (a) 71 Assuming Yu-f(ai) eu for some function f and that the eu are iid N (0,o2), how would you settle the dispute between John and Mary? Are either of them using correct reasoning to support their claims? (b) I10) What method(s) would you suggest to John and Mary to test for the straight line model? (C) S Suppose that there had been no replication (m hat guidance, if any, could you provide to John and Mary

Explanation / Answer

(b):

John & Mary must test the validity of the model by checking the F-statistics. F-stat is the measure of validity of the model. It is the ratio between SSR (Sum of square due to regression) and SST (total sum of square). More the value of F better the model is. In order to test of its significant, we need to perform hypothesis testing using ANOVA. ANOVA hypothesises that regression model is 'useless'. And, the rejection (based on low p-value or high F-stat), we can conclude that regression model is 'useful'.

(c):

Regression needs large sample size for its normalityassumptions and small sample size will violate this. So regression is not recommended.

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