Question

1. A professor examined the relationship between the number of hours devoted to reading, each week Y and the independent variable social class X1), the number of years of school completed x2 and reading speed X3, in pages read per hour. The following ANOVA table obtained from a stepwise regression procedure for a sample of 19 women over 60. A) Fill in the missing values. DESS Source Regression x3 MS P value 1 1058.628 Residual 585.02 Regression X2 X3 183.743 Residual 16 401.282 Regression X1/X2, X3 1 37.982 Residual 15 363.3 B) Test the hypothesis: Ho: B1 = B2 = 0 in the model Y = Bo + B1X1 + B2X2 + B3X3 +E VS H1: B1+0, B2 #0 F(X1, X2 X3) = ( SS(X1,x2,X3) - SS(X3))/2 = (183.743+37.982)/2 = 221.725/2 = 4.577 MSE(X1,x2,X3) 363.3/15 24.22 Find the p-value: What is your conclusion? C) Why can't we test for HO: B1= B3= 0 in the model Y = Bo + B1X1 + B2X2 + B3X3 + E The test statistic is F(X1, X3X2) = ?? explain why this is not possible D) Base on the results of 1A, B and C what is the appropriate model?

Answer 1

MS F . P-value source Regression x3 Residual of l ss 1058628 47 58500236.4132 30.76 0.01 Regression x2)x3. Residual 16 183-743 401.282 25.08 76326 0.05 Regression X1/X2,33 Residual l 15 37.982 363-3 | 21:22 981 01 (8) Tet H, 1B, P, ºo , the model y = $o+B,X, +B,*+ B3X3+E The null and alternative hypothesis :- Ho : B = B2 = 0 Ho: B, – B, 70 ( atleast one B, is non-zeno) from above table we can calculate values Ofis Regression ss (x1,42,43) – Regression ss (X2) - (1058-628 +183•743 +37.982)- (1058.628) = 221.725

Residual Ms («,, X2, X3) = 363-300 IS = 24.22 Calculate Value of F:- F(x,, Xe] X3) - Regression SS(X, 9X2,83) – Reg.s&;) 2 ( Residual MS (X, X 2 = 221725 Estats has an F distribution with I 24.22 n-p-2=19-2-2 - 15 = 4:577 F value for the calculated value 40577 Under the degrees of freedom (I, 15) is p=0.0193 Theis, p-value satisfying 0.0252 P2O.OS. Fine-2,1-a = fui5.0975 = 6.20 Fin-p-2,1-a = Finis, 0.95 = 4:54

So, reject null hypothesis and conclude that the addition of . x,, X, after accounting for X3 significantly adds to the prediction of y at the significance level 0.025 and Ooos. Hence, least one of the x, and X₂ are Significant given that Xz in the model, le. This difference is considered to be statistically Significant © are Hoi B.- B.-0 is not suitable by using ANOVA Table. The null and hypothesis alternative Ho iB, = B₂=0 Heiß, =B3 to ( Atleast one ß, is non- Zero), from the above data the value of Regression (X2) has not present. So, not able to proceed with the hypothesis Hoi B, =B30.

1 From the results of Table , B and a the appoopalate model is ý = B.+BX2+B3 3 Because from the part (a) (b) and (c) are the independent variable.. X and X₃ are significant 1 x is not significant So, exclude the variable (x) in the model. Hence, appropriate model is } = Bot B2 X ₂ + 8 3X3. * * * THANKING You *** * * * * PLS HKEų support ***