A study in Alachua County, Florida, investigated an index of mental health impairment, which had y = 27.3 and s = 5.5. Two explanatory variables were x1 = life events score (mean = 44.4, s = 22.6) and x2 = SES (socioeconomic status, mean = 56.6, s = 25.3). Life events is a composite measure of the number and severity of major life events, such as death in the family, that the subject experienced within the past three years. SES is a composite index based on occupation, income, and education. The table shows data for 6 subjects. The complete data 1 for a random sample of 40 adults in the county is in the Mental Health data file on the text CD. Some regression results are also shown.
a. Find the 95% confidence interval for β1.
b. Explain why the interval in part a means that an increase of 100 units in life events corresponds to anywhere from a 4- to 17-unit increase in mean mental impairment, controlling for SES. (This lack of precision reflects the small sample size.)

Transcribed Image Text:

y mental impairment, xi-life events index. and rsocioeconomic status Ху Ху 17 46 84 26 50 4030 4453 19 39 97 26 4852335 38 Predictor Constant life ses S 4. 55644 R-Sq-33 . 9% Coef 28. 230 SE Coef 2.174 0.10326 0.03250 0.09748 0.02908 12.98 0.000 3.18 0.003 3.35 0.002 Based on a larger survey reported in a Ph.D. thesis by C. E. Holzer III at University of Florida. Analysis of Variance Source Regression 394.24 197.12 9.49 0.000 Res. Error 37 768.16 20.76 Total DE MS 39 1162.40