chapter seven

chapter seven The Two-Variable Model: Hypothesis Testing

Figure 7-1 Conditional distribution of disturbances ui.

Figure 7-2 (a) Homoscedasticity (equal variance);(b) Heteroscedasticity (unequal variance).

Figure 7-3 Patterns of autocorrelation: (a) No autocorrelation;(b) positive autocorrelation; (c) negative autocorrelation.

Table 7-1 Computations for the lotto example.

Table 7-2 Monte Carlo experiment: Yi =1.5 + 2Xi +ui; u ~ N(0, 4).

Figure 7-4 (Normal) sampling distributions of b1 and b2.

Figure 7-5 (a) 95%confidence interval for B2 (8 d.f.); (b) 95% confidence interval for the slope coefficient of the Lotto example.

Figure 7-6 The t distribution for 8 d.f.

Figure 7-7 One-tailed t test: (a) Right-tailed; (b) left-tailed.

Figure 7-8 Breakdown of total variation Yi.

Figure 7-9 Actual and fitted Y values and residuals for the Lotto example.

Table 7-3 Indexes of compensation and productivity in the U.S. business sector, 1059-2000.

Figure 7-10 Relationship between compensation and productivity in the U.S. business sector, 1959-2000.

Figure 7-11 Actual Y, estimated Y and residuals (Regression of compensation on productivity).

Figure 7-12 Histogram of residuals from the compensation-productivity regression.

Figure 7-13 Normal probability plot of residuals obtained from the compensation-productivity regression.

Figure 7-14 95% confidence band for the true Lotto expenditure function.

Table 7-4 Capacity utilization and inflation in the United States, 1970-2001.

Table 7-5 Cash dividend (Y) and after-tax profits (X) in U.S. manufacturing industries, 1974-1986.

Table 7-6 U.S. expenditure on imported goods (Y) and personal disposable income (X), 1968-1987*.