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14.25 A teacher wants to check if there was a linear association between the final grade, the number of absences, and gender (s-0 for female, s-1 for male). Treating his class of 100 students as a random sample, Minitab returned the following output

Answer 1

Answer

(a) Null hypothesis must state that there is no linear dependency, means $\beta {_{1}}=\beta{_{2}} =0$

And alternative hypothesis must state that there is at least one linear dependency, means at least one coefficient is not equal to 0

So, option B is correct

(b) Yes, null is rejected because the p value corresponding to the regression is 0.000 which means it is significant at alpha level 1%.

so option A is correct because we need to check it for 1%

(c) The regression equation is already given in the data output table, but the p value corresponding to absences is not significant because its more than 0.01 alpha level, so we will avoid it in parsimonious regression equation.

so, parsimonious regression equation is

Grade= 73.12 + 7.66*sex

this means that the option C is correct

(d)

we have the parsimonious regression equation  

Grade= 73.12 + 7.66*sex

we have to find the Grade score when sex = 1 for male, we get

Grade= 73.12+ (7.66*1) =  80.78 is the required grade