Practice Homework 12 Solutions See answers at the back of the book. The points in the scatterplot are in stacks because there are only 4 different values of the explanatory variable, and 4 observations taken at each. The 90% confidence interval for the slope was produced in SAS with the "clb alpha = 0.10" option on the model statement. We are 90% confidence that the population slope beta is between 0.00424 and 0.01289. Thus we are very confident that the slope is positive, which is evidence that increasing availability of prey increases the proportion killed. The regression standard error s is what SAS calls the "Root MSE." The 90% confidence interval for the mean proportion of prey killed when 40 are available is obtained with the "clm alpha = 0.10" option. Since observations numbered 9 - 12 in the dataset have 40 as the value of the explanatory variable, we find the needed confidence interval in those rows in the columns headed "90% CL Mean." The interval is ( 0.3741, 0.5524) options linesize = 72 ; data preypred ; infile '/group/ftp/pub/kcowles/datasets/preypred.dat' ; input perch killed ; run ; proc plot data = preypred ; plot killed * perch = '.' ; run ; proc reg data = preypred ; model killed = perch / clb cli clm alpha = 0.10 ; run ; The SAS System 1 15:02 Thursday, May 8, 2008 Plot of killed*perch. Symbol used is '.'. killed | | 0.825 + . 0.800 + 0.775 + 0.750 + 0.725 + . 0.700 + . 0.675 + 0.650 + 0.625 + 0.600 + . . 0.575 + 0.550 + . 0.525 + . 0.500 + 0.475 + 0.450 + 0.425 + 0.400 + 0.375 + 0.350 + 0.325 + 0.300 + . . . 0.275 + 0.250 + 0.225 + 0.200 + . 0.175 + 0.150 + 0.125 + 0.100 + . 0.075 + . 0.050 + 0.025 + 0.000 + . | --+-----------+-----------+-----------+-----------+-----------+-- 10 20 30 40 50 60 perch NOTE: 2 obs hidden. The SAS System 2 15:02 Thursday, May 8, 2008 The REG Procedure Model: MODEL1 Dependent Variable: killed Number of Observations Read 16 Number of Observations Used 16 Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 1 0.43327 0.43327 12.18 0.0036 Error 14 0.49804 0.03557 Corrected Total 15 0.93131 Root MSE 0.18861 R-Square 0.4652 Dependent Mean 0.39900 Adj R-Sq 0.4270 Coeff Var 47.27097 Parameter Estimates Parameter Standard Variable DF Estimate Error t Value Pr > |t| Intercept 1 0.12049 0.09269 1.30 0.2146 perch 1 0.00857 0.00246 3.49 0.0036 Parameter Estimates Variable DF 90% Confidence Limits Intercept 1 -0.04277 0.28375 perch 1 0.00424 0.01289 The SAS System 3 15:02 Thursday, May 8, 2008 The REG Procedure Model: MODEL1 Dependent Variable: killed Output Statistics Dependent Predicted Std Error Obs Variable Value Mean Predict 90% CL Mean 1 0 0.2062 0.0726 0.0783 0.3341 2 0.1000 0.2062 0.0726 0.0783 0.3341 3 0.3000 0.2062 0.0726 0.0783 0.3341 4 0.3000 0.2062 0.0726 0.0783 0.3341 5 0.2000 0.2919 0.0563 0.1928 0.3910 6 0.3000 0.2919 0.0563 0.1928 0.3910 7 0.3000 0.2919 0.0563 0.1928 0.3910 8 0.6000 0.2919 0.0563 0.1928 0.3910 9 0.0750 0.4633 0.0506 0.3741 0.5524 10 0.3000 0.4633 0.0506 0.3741 0.5524 11 0.6000 0.4633 0.0506 0.3741 0.5524 12 0.7250 0.4633 0.0506 0.3741 0.5524 13 0.5170 0.6347 0.0824 0.4896 0.7797 14 0.5500 0.6347 0.0824 0.4896 0.7797 15 0.7000 0.6347 0.0824 0.4896 0.7797 16 0.8170 0.6347 0.0824 0.4896 0.7797 Output Statistics Obs 90% CL Predict Residual 1 -0.1498 0.5622 -0.2062 2 -0.1498 0.5622 -0.1062 3 -0.1498 0.5622 0.0938 4 -0.1498 0.5622 0.0938 5 -0.0548 0.6385 -0.0919 6 -0.0548 0.6385 0.008119 7 -0.0548 0.6385 0.008119 8 -0.0548 0.6385 0.3081 9 0.1193 0.8072 -0.3883 10 0.1193 0.8072 -0.1633 11 0.1193 0.8072 0.1367 12 0.1193 0.8072 0.2617 13 0.2722 0.9972 -0.1177 14 0.2722 0.9972 -0.0847 15 0.2722 0.9972 0.0653 16 0.2722 0.9972 0.1823 Sum of Residuals 0 Sum of Squared Residuals 0.49804 Predicted Residual SS (PRESS) 0.61978