ANSWER:
(a)
Claim 1:
H0: Coefficient of Female = 0
H1: Coefficient of Female
0
Test Statistic, t = -6.52 / 5.52 = -1.8
Degree of freedom = n - k - 1 where n is number of observations, k is number of predictors
= (29 + 81) - 3 - 1 = 106
Critical value of t at significance level of 0.05 and df = 106
is,1.98
As, observed t is not less than -1.98 or greater than 1.98, we fail to reject H0 and conclude that there is no significant evidence that the variable Female is significant in the model.
H0: Coefficient of Sibs = 0
H1: Coefficient of Sibs
0
Test Statistic, t = 0.51/ 2.25 = 0.2267
As, observed t is not less than -1.98 or greater than 1.98, we fail to reject H0 and conclude that there is no significant evidence that the variable Sibs is significant in the model.
For testing simultaneously, number of hypothesis test is 2.
H0: Coefficient of Female = 0
H1: Coefficient of Sibs = 0
Using Boneferroni correction, Significance level = 0.05/2 = 0.025
Critical value of t at significance level of 0.025 and df = 106
is,
2.27
As, observed t for both the hypotheses is not less than -2.27 or greater than 2.27, we fail to reject H0 and conclude that there is no significant evidence that the variable female and Sibs are significant in the model.
(b)
For F test,
Numerator degree of freedom = Number of variables in reduced model , k = 2
Denominator degree of freedom = n - k - 1= (29 + 81) - 2 - 1 = 107
Critical value of F for significance level of 0.05 and DF = 2, 107 is 3.08
As, observed F (0.84) is less than the critical value, we fail to reject H0 and conclude that there is no significant evidence that the variable Sibs or Female is significant in the model.
(c)
For Full model,
Numerator degree of freedom = Number of variables in full model , k = 3
Denominator degree of freedom = n - k - 1= (29 + 81) - 3 - 1 = 106
Critical value of F for significance level of 0.05 and DF = 3, 106 is 2.69
As, observed F (57.25) is less than the critical value, reject H0 and conclude that there is significant evidence that the model is significant and there is significant relationship between weight and height.
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Weight
Male
73.84701702
241.8935632
Male
68.78190405
162.3104725
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74.11010539
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167.9711105
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67.01894966
175.9294404
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63.45649398
156.3996764
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71.19538228
186.6049256
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71.64080512
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