Dr. Susan Sweeney, a Providence, Rhode Island, psychologist, specializes in trea

Question

Dr. Susan Sweeney, a Providence, Rhode Island, psychologist, specializes in treating patients who are agoraphobic (i.e., afraid to leave their homes). The following table indicates how many patients Dr. Sweeney has seen each year for the past 5 years. It also indicates what the robbery rate was in Providence during the same year Year Number of Patients Robbery Rate 89 101.1 94.8 103.3 116.2 per 1000 Population 2 55 60 54 58 61 a) Using the data in above table, apply linear regression to study the relationship between the robbery rate and Dr. Sweeney s patient load. (2 points) b) If the robbery rate increases to 139.2 in year 11, how many phobic patients will Dr. Sweeney treat? If the robbery rate drops to 70.6, what is the patient projection? (2 points) c) How well does the model fit the data? Show your work. (2 points)

Explanation / Answer

a) The general form of linear regression is y = b0 + b1 X

where b0 is the intercept and b1 is the slope

y = 31.97 + 0.254 X

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b) If the robbery rate increases to 139.2, the number of patients treated = 31.97 + 0.254 * 139.20

  Number of patients treated = 67.33

If the robbery rate drops to 70.6, the patient projection = 31.97 + 0.254 * 70.6

Patient projection = 49.90

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c) The R squared value—the coefficient of determination—represents the proportion of the variation that is accounted for in the dependent variable by the whole set of independent variables .An Rsquared value of 1.0 would mean that the X variables as a set perfectly predicted the Y (the dependent variable). An R-squared value of zero would indicate that the X variable as a set did not predict the Y variable at all. An R squared value of 0.72627 indicates that the data points fits well into the regression line.

SUMMARY OUTPUT Regression Statistics Multiple R 0.852219033 R Square 0.72627728 Adjusted R Square 0.635036374 Standard Error 1.842325086 Observations 5 ANOVA df SS MS F Significance F Regression 1 27.01751 27.01751 7.959996 0.066664 Residual 3 10.18249 3.394162 Total 4 37.2 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 31.97451207 9.120008 3.505974 0.039312 2.950575 60.99845 2.950575 60.99844904 X Variable 1 0.254019508 0.090035 2.821347 0.066664 -0.03251 0.540551 -0.03251 0.540550577

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