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Call: glm(formula = Y ~ X1 + X3 + X4, family = poisson(), data = geriatric) Deviance Residuals: Min 1Q Median 3Q Max -2.2152 -0.7512 -0.2594 0.5830 2.2893 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 0.443890 0.317289 1.399 0.16181 X1 -1.077770 0.131415 -8.201 2.38e-16 *** X3 0.009471 0.002957 3.203 0.00136 ** X4 0.008979 0.004190 2.143 0.03209 * --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 (Dispersion parameter for poisson family taken to be 1) Null deviance: 199.19 on 99 degrees of freedom Residual deviance: 108.94 on 96 degrees of freedom AIC: 375.44 Number of Fisher Scoring iterations: 5 (Intercept) X1 X3 X4 0.44389020 -1.07777033 0.00947114 0.00897921 Residual deviance = 108.9409 on 96 df Dispersion parameter = 1
Adi S.
The next two questions refer to the following situation: One concern about the depletion of the ozone layer is that the increase in UV light will decrease crop yields. An experiment was conducted in a green house where soybean plants were exposed to varying levels of UV levels - measured in Dobson units. At the end of the experiment the yield (kg) was measured. A regression analysis was performed in STATA with the following results: yield | Coef. | Std. Err. | t | P>|t| | [95% Conf. Interval] ---|---|---|---|---|--- uv | -0.046285 | 0.010741 | *hidden* | 0.0008 | ****hidden**** _cons | 3.9800118 | 0.053774 | 74.01 | 0.0000 | 3.8638398 4.0961838 5. Write down the estimated least squares regression line. 6. Refer to the output above. Explain which of the following correctly presents the null and alternate hypotheses for a significance test of the slope, the test statistic, and the p- value: (a) H0:βuv = 0; H1:βuv ≠ 0; T-stat = -4.31; p-value = .0000. (b) H0:β0 = 0; H1:β0 < 0; T-stat = -74.01; p-value < .0001. (c) H0:βuv = 0; H1:βuv < 0; T-stat = -4.31; p-value = .0004. (d) H0:βuv = 0; H1:βuv < 0; T-stat = -4.31; p-value = .0008.
Consider the Galapagos data and model analyzed in this chapter: The purpose of this question is to reproduce the details of the GLM fitting of this data. a) Fit a Poisson model to the species response with the five geographic variables as predictors. Do not use the endemics variable. Report the values of the coefficients and the deviance. b) For a Poisson GLM, derive ̗, d̗/d̔, V(̔) and the weights to be used in an iteratively fit GLM. What is the form of the adjusted dependent variable here? c) Using the observed response as initial values, compute the first stage of the iteration, stopping after the first linear model fit. Compare the coefficients of this linear model to those found in the GLM fit. How close are they? d) Continue the iteration to get the next ̗ and ̔. Use this to compute the current value of the deviance. How close is this to the deviance from the GLM? e) Compute one more iteration of the GLM fit, reporting the next calculation of the coefficients and deviance. How close are these to the target now? f) Repeat these iterations a few more times, computing the deviance each time. Stop when the deviance does not change much. Compare your final estimated coefficients to those produced by the GLM fit. g) Use your final iterated linear model fit to produce standard errors for the coefficients. How close are these to those produced by the direct GLM fit?
Shaiju T.
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