Question 6. We have two sets of data, A and B, involving values of X and Y, but

Question

Question 6. We have two sets of data, A and B, involving values of X and Y, but we are not sure whether to fit the data separately or together. We fitted the six-parameter model where Z is a dummy variable whose value is 0 for "set A" and 1 for "set B." 25 (a) What hypothesis would you test whether a single straight model line fits all the data? If you can test this hypothesis using the following Tables 1, 2 and 3, conduct the test at the 5% significance level (b) What hvpothesis would vou test whether two separate parallel quadratic lines fit all the data? If you can test this hypothesis using the following Tables 1, 2, and 3 conduct the test at the 5% significance level

Explanation / Answer

a. We will test the hypothesis

H0: 0= 1= 2=0= 1= 2=0

vs H1: at least one of the parameters0

From the third Anova table we can conduct a F test to test this hypothesis.

F=Mean ss from Model/ Mean ss from Error ~F dist with df 5,9

F= [19.62/5]/[0.41/9]= 86.136

Now Tabulated Fat df 5,9 at 1% level of significance is 6.056 < 86.136 Hence Ho is rejected

So, The model is statistically significant so,one single model can fit in the data.

b.To check the reverse, we need to test two sets of hypotheses.

1. H0: 0= 1=0=0

vs H1: at least one of the parameters0

From the first Anova table we can conduct a F test to test this hypothesis.

F=Mean ss from Model/ Mean ss from Error ~F dist with df 2,12

F= [18.78/2]/[1.25/12]= 90.144

Now Tabulated Fat df 2,12  at 1% level of significance is 6.926 < 86.136 Hence Ho is rejected

So, The model is statistically significant so,a model on data A separtely would work

2. We will test the hypothesis

H0: 0= 1= 2=0=0

vs H1: at least one of the parameters0

From the third Anova table we can conduct a F test to test this hypothesis.

F=Mean ss from Model/ Mean ss from Error ~F dist with df 3,11

F= [18.79/3]/[1.24/11]= 55.56

Now Tabulated Fat df 3,11 at 1% level of significance is 6.216< 55.56 Hence Ho is rejected

So, The model is statistically significant so, A model on data B only would also work

Overall, any of the aporoaches would be statistically significant. Lets have a look at the Rsqs of the models to find out the best. Rsq=SSM/(SSM+SSE)

Form Table 1, Rsq=93.8; From Table 2, Rsq= 93.8, From Table 3, Rsq= 98.0

Hence, fittng a single model would be best.

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