The regression of equation (11.43), with standard errors, is

(a) Demonstrate, either with confidence intervals or two-tailed hypothesis tests, that b is statistically significant.

(b) The quadratic specification of this regression yields

Interpret the signs and values of bâ•›1 and bâ•›2 following the analysis of section 13.3.

(c) For this regression, SD(bâ•›1) = 1.125 and SD(bâ•›2) = .00846. Are either of these slopes statistically significant? Does the answer to this alter or confirm the interpretations of part b?

(d) The Râ•›2 value for this regression is .3865. Test the null hypothesis Hâ•›0 : β1€= 0 and β2 = 0 using equation (12.35). What can we conclude about the joint effects of the variable measuring rural access to water and its square on child mortality? Comparing this conclusion to that of part

c, what can we conclude about the relationship between these two variables?

(e) Use equation (12.36) to derive the correlation between bâ•›1 and bâ•›2.
(fâ•›) Equation (11.43), with the linear explanatory variable replaced by the quadratic explanatory variable, is

Is b statistically significant?
(g) Compare equation (11.43), the quadratic specification in part

b, and the bivariate regression in part

f. In addition to what we’ve already learned about these regressions in this exercise, their Râ•›2 values are, respectively, .3754, .3865, and .3864. Which regression seems to be the most compelling way to represent the information in the sample? Why? Predict the child mortality rates for water accessibility rates of 30%, 60%, and 90% using each of the regressions. Does it make much difference which Â�regression we use? Why or why not?

Transcribed Image Text:

child mortality=200.5-1.764 percentage of rural population with access to improved water + e.. (14.66) (.1973)