... test of H0: β0 = 0 tell us that β0 is statistically significantly larger than zero.

The t-statistic and p-value in the second row of Table 21.1 test the null hypothesis H0: β1 = 0; this test considers the population slope rather than the intercept. The t-statistic in this row shows that b1 lies b1/se(b1) = 16.37 standard errors above zero. That’s unlikely to happen by chance if the null hypothesis H0: β1 = 0 is true, so the p-value is tiny (less than 0.0001). In plain language, the t-statistic tells us that the incremental production time is not zero. That’s not a surprise; even an automated manufacturing process takes some time to produce a custom product.

A typical reaction to these tests of the intercept and slope is to wonder why software automatically ...

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