Question

QUESTION 19

1.       Polynomial regression was used to predict sales (Y) using advertising expenditure (X) and its square (X²) as independent variables. The following information is available:
   

   Predictor	Coefficients	Standard Error
   Constant	328.42	29.42
   X	10.970	1.832
   X2	-.12507	.02586
   ANOVA
   Source	DF	SS		F
   Regression				42.56
   Residual
   Total	11	14,107.7

   
   Testing, at the .05 level of significance, if the quadratic term is useful for the prediction of sales, the alternative hypothesis is:

   	a.	Ha:  b1 ¹ 0
   	b.	Ha:  b2 = 0
   	c.	None of these alternatives is correct.
   	d.	Ha:  b2 ¹ 0
   	e.	Ha:  b1 = 0

Answer 1

The .05 level of significance, if the quadratic term is useful for the prediction of sales, the alternative hypothesis is:

OPTION B- Ha : b2 = 0

b2 represents the coefficient of the quadratic variable. It is not a square itself, its just a coefficient which can take any value. We have to test whether the quadratic term is useful, for the same we need to test whether the coefficient of the quadratic term is 0 or not.

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