Occasionally an investigator may wish to compute a confidence interval for

a, the y intercept of the true regression line, or test hypotheses about

a. The estimated y intercept is simply the height of the estimated line when x 5 0, since a 1 b(0) 5

a. This implies that sa the estimated standard deviation of the statistic

a, results from substituting x* 5 0 in the formula for sa1bx*.

The desired confidence interval is then a 6 1t critical value2sa and a test statistic is t 5 a 2 hypothesized value sa

a. The article “Comparison of Winter-Nocturnal Geostationary Satellite Infrared-Surface Temperature with Shelter-Height Temperature in Florida” (Remote Sensing of the Environment [1983]: 313– 327)

used the simple linear regression model to relate surface temperature as measured by a satellite (y) to actual air temperature (x) as determined from a thermocouple placed on a traversing vehicle. Selected data are given (read from a scatterplot in the article).

x 22 21 0 1 2 3 4 y 23.9 22.1 22.0 21.2 0.0 1.9 0.6 x 567 y 2.1 1.2 3.0 Estimate the population regression line.

b. Compute the estimated standard deviation sa. Carry out a test at level of significance .05 to see whether the y intercept of the population regression line differs from zero.

c. Compute a 95% confidence interval for

a. Does the result indicate that a 5 0 is plausible? Explain.