Table 11.19 shows results of regressing y = birth rate (number of births per 1000 population) on x1 =

women’s economic activity and x2 = literacy rate, using UN data for 23 nations.

(a) Report the value of each of the following:

(i) ryx1, (ii) ryx2, (iii) R2,

(iv) TSS, (v) SSE, (vi) mean square error,

(vii) s, (viii) sy, (ix)se for b1,

(x) t for H0: β1 = 0,

(xi) P for H0: β1 = 0 against Ha: β1 = 0,

(xii) P for H0: β1 = 0 against Ha: β1

(xiii) F for H0: β1 = β2 = 0,

(xiv) P for H0: β1 = β2 = 0.

(b) Report the prediction equation, and interpret the signs of the estimated regression coefficients.

(c) Interpret the correlations ryx1 and ryx2.

(d) Report R2, and interpret its value.

(e) Report the multiple correlation, and interpret.

(f) Though inference may not be relevant for these data, report the F statistic for H0: β1 = β2 = 0, report its Pvalue, and interpret.
(g) Show how to construct the t statistic for H0: β1 = 0, report its df and P-value for Ha: β1 = 0, and interpret.

Transcribed Image Text:

TABLE 11.19 BIRTHS Mean 22.117 Std Deviation 10.469 23 ECON 47.826 19.872 LITERACY 77.696 17.665 wwwz N 23 23 Correlations BIRTHS ECON Correlation BIRTHS 1.00000 -0.61181 LITER -0.81872 ECON -0.61181 1.00000 0.42056 LITERACY -0.81872 0.42056 1.00000 Sum of Squares DF Mean Square F Sig Regression 1825.969 2 912.985 31.191 0.0001 Residual 585.424 20 29.271 Total 2411.393 22 Root MSE (Std. Error of the Estimate) 5.410 Unstandardized Coeff. R Square 0.7572 B Std. Error Standardized Coeff. (Beta) t (Constant) 61.713 5.2453 11.765 Sig 0.0001 ECON -0.171 0.0640 -0.325 -2.676 0.0145 LITERACY -0.404 0.0720 -0.682 -5.616 0.0001