Download ANCOVA Quiz Answers: Weight Change of Baby Snow Geese and more Quizzes Data Analysis & Statistical Methods in PDF only on Docsity! STAT 516 Quiz 7 Answers 1) Give the model equation for the equal slopes ANCOVA, identifying any parameters used. 2) Give the estimates for the parameters in the model equation in (1), including the estimated standard deviation of the errors. yij = β0 + β1xij + τi + εij where yij is the weight change of the jth goose in diet group i (either plants or duck chow) β0 is the intercept for the baseline group (-1.9652) β1 is the slope for the digestive efficiency (0.0668) xij is the digestive efficiency of the jth goose in diet group i (2.3987 for Chow, Plants is baseline) τi is the effect of being in diet group i (2.3987 for Chow, Plants is baseline) εij is the error for the jth goose in diet group i (root MSE is 3.8541) 3) Does the assumption of equal slopes ANCOVA seem to be met for this data set? How could you tell? Yes, we fail reject the null hypothesis that the interactions are all zero (slopes are equal) with a p-value of 0.5081. 4) Which plot do we use to verify that the variances of the errors are constant? Briefly sketch what that plot would look like if the assumption isn’t met. Residual vs. predicted. A fan shape that is wider on one end than the other would be one example, < or > . 5) Does diet appear to have an effect on the weight gain of baby snow geese? Yes. We reject the null hypothesis that τchow=τplant at α=0.05 with a p-value of 0.0486. (You would say no if you used a=0.01.) 6) and If x=1, what is the estimated probability that Y=1? 1/(1+e-1)=.731 Parameter Information Parameter 1 2 3 4 Variable Intercept digeffic diet diet Chow Plants Model Equation wchange = - 1.9652 + 0.0668 digeffic + 4.8836 P_3 Summary of Fit Mean of Response 1.0952 Root MSE 3.8541 R-Square 0.4349Adj R-Sq 0.4059 Analysis of Variance Source Model Error C Total DF 2 39 41 Sum of Squares 445.8113 579.3078 1025.1190 Mean Square 222.9056 14.8540 F Stat 15.01 Pr > F <.0001 Type III Tests Source digeffic diet DF 1 1 Sum of Squares 31.2630 61.5683 Mean Square 31.2630 61.5683 F Stat 2.10 4.14 Pr > F 0.1548 0.0486 Parameter Estimates Variable Intercept digeffic diet diet Chow Plants DF 1 1 1 0 Estimate -1.9652 0.0668 4.8836 0 Std Error 1.1865 0.0460 2.3987 . t Stat -1.66 1.45 2.04 . Pr >|t| 0.1057 0.1548 0.0486 . Tolerance . 0.3651 0.3651 . Var Inflation 0 2.7393 2.7393 . 0 2 4 6 P_wchange -5 0 5 R _ w c h a n g e -2 0 2 RN_wchange -5 0 5 R _ w c h a n g e Type III Tests Source digeffic diet digeffic*diet DF 1 1 1 Sum of Squares 2.8655 22.1626 6.7252 Mean Square 2.8655 22.1626 6.7252 F Stat 0.19 1.47 0.45 Pr > F 0.6652 0.2327 0.5081 0ˆ0 =β 11̂ =β
