Discussion
Which of the following hypotheses are tested by a regression function ?
Answer: D
A regression function tests all three kinds of hypothesis listed: whether the inter-relation between variables is significantly different from zero, whether the degree and direction of the relation are non-zero with a satisfactory goodness of fit, and whether the influence of systematic explanatory factors is greater than, lesser than or equal to the influence of random factors. These correspond to tests on the coefficients, the R squared, and the F test comparing explained with unexplained variation. Since each of A, B and C is a valid hypothesis, the keyed answer is option D.
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