Tutorial 4 HE204b

# Tutorial 4 HE204b - 7.7(a No An r-value cannot exceed 1 in...

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Unformatted text preview: 7.7 (a) No. An r-value cannot exceed 1 in absolute value. Plugging the given data in Eq. (7.11.2), the reader can should verify that: r113 = 2.295, which is logically impossible. (b) Yes. Following the same procedure as in (a), the reader will find that r113 = 0.392, which is possible. (c) Yes, again it can be shown that r113 = 0.880, which is possible. 7.10 (o) 3: (b) If you multiply X; by 2, you can verify from Equations (7.4.7) and (7.4.8), that the slopes remain unaffected. On the other hand, if you multiply Y by 2, the slopes as well as the intercept coefﬁcients and their standard errors are all multiplied by 2. Always keep in mind the units in which the regressand and regressors are measured. 7.11 From (7.11.5) we knowr that R: = all + a: - 2mm _ 1— I"; Therefore? when r23 = D, that is, no correlation between variables X2 and X3, 11'?2 = r212 + r213, that is, the multiple coefﬁcient of determination is the sum of the coefﬁcients of determination in the regression of I" on X2 and that of Y on X3. 8.1 (a) In the ﬁrst model, where sales is a linear function of time, the rate of change of sales, (dedt) is postulated to be a constant, equal to {31, regardless of time I. In the second model the rate of change is not constant because (dedt) = or, + 2052:, which depends on time I. (b) The simplest thing to do is plot Y against time. If the resulting graph looks parabolic, perhaps the quadratic model is appropriate. (c) This model might be appropriate to depict the earnings proﬁle of a person. Typically, when someone enters the labor market, the entry-level earnings are low. Overtime, because of accumulated experience, earnings increase, but after a certain age they start declining. (d) Look up the web sites of several car manufacturers, or Motor Magazine, or the American Automobile Association for the data. 8.6 Start with equation (8.5.11) and write it as: —k R1 F = m ., which can be rewritten as: k —1 R?- F E 3%)) = (1 R2) . after further algebraic manipulation, we n _ _ obtain R2 FUc _1) , which is the desired result. _ F(k—1)+(n—k) For regression (8.2.1), n=64, k = 3. Therefore, F @3152} = 3.15.. approx. (Note use 60 df in place of 62 df). Therefore, putting these values in the preceding R2 formula, we obtain: RZ- 2(3.15) =6.3c=m,}936 _ 2(3.15)+61 67.3 This is the critical R2 value at the 5% level of signiﬁcance. Since the observed of R2 of 0.7077 in (8.2.1) far exceeds the critical value, we reject the null hypothesis that the true li’2 value is zero. 7.24 (a) CI = —20.6327 + 0.7 340 Yd + 0.0360Wea3rh — 5.5212 Interest r= (—1.6085) (53.3762) (14.4882) (2.306?) a2 = 0.9994 (b) The three independent variables are statistically signiﬁcant at the 5% level. It seems that increases in Income (Yd) and Wealth are related to increases in Ccnsumptien, whereas an increase in the Interest rate corresponds tc a decrease in the Ccnsumpticn level. This makes sense. Dependent Variable: C01 Method: Least Squares Date: 02703709 Time: 17:14 Sample: 1947 2000 Included observations: 54 WEALTH INTEREST R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F—statistic) Coefﬁcient 0.734028 0.035976 —5.521224 —20.63274 0.999402 0.999366 37.79877 71437.35 —270.6877 27838.41 0.000000 Std. Error t-Statistic 0.013752 53.37622 0.002483 14.48822 2.306675 —2.393 585 12.82699 —1.608541 Mean dependent var SD. dependent var Akaike info criterion Schwarz criterion Harman—Quinn criter. Durbin—Watson stat Prob. 0.0000 0.0000 0.0205 0.1140 2888.356 1500.903 10.17362 10.32095 10.23044 1.310554 ...
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