13.28 Regression for human development A study investigated an index of human development in a South American country, which had y = 27.3 and s = 5.5. Two explanatory variables were x1 = literacy rate in percentage

(mean = 44.4, s = 22.6) and x2 = daily per capita income in dollars (mean = 56.6, s = 25.3). Based on a random sample of 50 cities in the country, some regression results are also shown as follows:

a. Find the 95% confidence interval for b1.

b. Explain why the interval in part a means that an increase of 10 units in literacy rate corresponds to anywhere from a 0.4- to 1.7-unit increase in mean human development, controlling for daily per capita income. (This lack of precision reflects the small sample size.)

y = index of human development, x = life literacy rate and dally per capita income Coefficients Term Coef SE Coef T-Value P-Value Constant 28.23 2.17 12.98 0.000 literacy 0.1033 0.0325 3.18 0.003 rate daily per -0.0975 0.0291 -3.35 0.002 capita income Model Summary S 4.55644 R-sq 33.92% Analysis of Variance. Source Regression Error Total m m DF SS MS F-Value P-Value 2 37 394.2 197.12 768.2 20.76 9.49 0.000 39 1162.4