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.

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?

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