Estimate the three multiple regression coefficients -

Question

Problem 1:

You are given the following data based on 15 observations:

Y‾ = 367.693; X₂‾ = 402.760; X‾₃ = 8.0; ∑y_i² = 66,042.269

∑x_2i² = 84,855.096; ∑x_3i² = 280.0; ∑y_ix_2i = 74,778.346

∑y_ix_3i = 4,250.9; ∑x_2ix_3i = 4,796.0

where lowercase letters, as usual, denote deviations from sample mean values.

a. Estimate the three multiple regression coefficients.

b. Estimate their standard errors.

c. Obtain R₂ and R‾².

d. Estimate 95% confidence intervals for B₂ and B₃.

e. Test the statistical significance of each estimated regression coefficient using α = 5% (two-tail).

f. Test at α = 5% that all partial slope coefficients are equal to zero. Show the ANOVA table.

Problem 2:

Table 4-7 (found on the textbook's Web site) gives data on child mortality (CM), female literacy rate (FLR), per capita GNP (PGNP), and total fertility rate (TFR) for a group of 64 countries.

a. A priori, what is the expected relationship between CM and each of the other variables?
b. Regress CM on FIR and obtain the usual regression results.
c. Regress CM on FLR and PGNP and obtain the usual results.
d. Regress CM on FIR, PGNP, and TFR and obtain the usual results. Also show the ANOVA table.
e. Given the various regression results, which model would you choose and why?
f. If the regression model in (d)is the correct model, but you estimate (a)or Alar (c), what are the consequences?
g. Suppose you have regressed CM on FLR as in (b). How would you decide if it is worth adding the variables PGNP and TFR to the model? Which test would you use? Show the necessary calculations.

Table 4-7
Child Mortality, Female Literacy Rate,
Per Capita GNP, and Total Fertility Rate for
64 Countries
CM	FLR	PGNP	TFR
128	37	1870	6.66
204	22	130	6.15
202	16	310	7
197	65	570	6.25
96	76	2050	3.81
209	26	200	6.44
170	45	670	6.19
240	29	300	5.89
241	11	120	5.89
55	55	290	2.36
75	87	1180	3.93
129	55	900	5.99
24	93	1730	3.5
165	31	1150	7.41
94	77	1160	4.21
96	80	1270	5
148	30	580	5.27
98	69	660	5.21
161	43	420	6.5
118	47	1080	6.12
269	17	290	6.19
189	35	270	5.05
126	58	560	6.16
12	81	4240	1.8
167	29	240	4.75
135	65	430	4.1
107	87	3020	6.66
72	63	1420	7.28
128	49	420	8.12
27	63	19830	5.23
152	84	420	5.79
224	23	530	6.5
142	50	8640	7.17
104	62	350	6.6
287	31	230	7
41	66	1620	3.91
312	11	190	6.7
77	88	2090	4.2
142	22	900	5.43
262	22	230	6.5
215	12	140	6.25
246	9	330	7.1
191	31	1010	7.1
182	19	300	7
37	88	1730	3.46
103	35	780	5.66
67	85	1300	4.82
143	78	930	5
83	85	690	4.74
223	33	200	8.49
240	19	450	6.5
312	21	280	6.5
12	79	4430	1.69
52	83	270	3.25
79	43	1340	7.17
61	88	670	3.52
168	28	410	6.09
28	95	4370	2.86
121	41	1310	4.88
115	62	1470	3.89
186	45	300	6.9
47	85	3630	4.1
178	45	220	6.09
142	67	560	7.2

Problem 3:

Refer to Example 4.5 (Table 4-6) about education, GDP, and population for 38 countries.

a. Estimate a linear (LIV) model for the data. What are the resulting equation and relevant output values (i.e., Fstatistic, t values, and R2)?

b. Now attempt to estimate a log-linear model (where both of the independent variables are also in the natural log format).

c. With the log-linear model, what does the coefficient of the GDP variable indicate about education? What about the population variable?

d. Which model is more appropriate?

Table 4-6
Education Expenditures, Gross Domestic Product, and population for Several Countries
Country	EDUC	GDP	POP
Algeria	1988	41969	27.45
Belgium	13020	232006	10.093
Chile	1393	50919	13.994
Colombia	1870	68631	35.178
Czech Republic	1993	39896	10.275
Denmark	10971	151266	5.207
Dominican Rep	123	10350	7.684
Ecuador	519	16606	11.221
Finland	6696	97624	5.085
Guatemala	194	12983	10.322
Hungary	2500	41506	10.162
Iran	2741	73414	66.671
Ireland	2810	52662	3.536
Malaysia	2980	72505	19.695
Mexico	18273	420788	89.564
Morocco	1452	30351	26.025
Myanmar	742	79127	44.323
Netherlands	17095	334286	15.382
New Zealand	3124	51320	3.519
Norway	9268	122926	4.314
Oman	398	12919	2.116
Peru	1739	50287	23.131
Poland	3430	92597	38.499
Portugal	4362	87352	9.824
Saudi Arabia	7313	120168	17.765
Singapore	1628	71039	3.268
Slovakia	535	13746	5.325
Slovenia	720	14386	1.925
Spain	21959	483652	39.577
Switzerland	13246	261388	7.104
Syria	1392	44753	13.84
Thailand	4337	145168	57.782
Tunisia	854	15626	8.82
Turkey	4173	135961	59.903
U Arab Emir	700	36666	2.157
Uruguay	392	16250	3.168
Venezuela	2825	58418	21.378
Yemen	1214	22380	14.329

Example 4.5. Expenditure on Education in 38 Countries:

Based on data taken from a sample of 38 countries (see Table 4-6, found on the textbook's Web site), we obtained the following regression:

Educ; = 414.4583 + 0.0523GDP_i - 50.0476 Pop

se = (266.4583) (0.0018) (9.9581)

t = (1.5538) (28.2742) (-5.0257)

p value = (0.1292) (0.0000) (0.0000)

R² = 0.9616; R‾² = 0.9594; F = 439.22; p value of F = 0.000

where Edue = expenditure on education (millions of U.S. dollars), GDP = gross domestic product (millions of U.S. dollars), and Pop = population(millions of people). As you can see from the data, the sample includes a variety Of countries in different stages of economic development.

It can be readily assessed that the GDP and Pop variables are individually highly significant, although the sign of the population variable may be puzzling. Since the estimated F is so highly significant, collectively the two variables, have a significant impact on expenditure on education. As noted the variable are also individually significant.

The R² and adjusted R‾² square values are quite high, which is unusual in a cross-section sample of diverse countries.

Attachment:- stata guide.pdf