13.62 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

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a(t critical value)s and a test statistic is t a-hypothesized value Sa a. The article "Comparison of Winter-Nocturnal Geo- stationary Satellite Infrared-Surface Temperature with Shelter-Height Temperature in Florida" (Re- mote Sensing of the Environment [1983]: 313-327) used the simple linear regression model to relate sur- face temperature as measured by a satellite (y) to ac- tual air temperature (x) as determined from a thermo- couple placed on a traversing vehicle. Selected data are given (read from a scatterplot in the article). y x -2 -3.9 -2.1 -1 0 -2.0 1 2 3 -1.2 0.0 1.9 4 0.6 x 5 6 7 1.2 3.0 y 2.1 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 dif- fers from zero. c. Compute a 95% confidence interval for a. Does the result indicate that a = 0 is plausible? Explain.