Refer to exercise 11.150 on page 648 of the textbook. In this homework assignmen

Question

Refer to exercise 11.150 on page 648 of the textbook. In this homework assignment, you will investigate the linear relationship between weight change (in %) and digestion efficiency (in %) in baby snow geese. Below are sample statistics calculated from the observed weight changes and plot, digestion efficiencies the 42 feeding trials in the sample. The scatterplot of the data, residual plot, and normal probability plot of the residuals are also provided. Use this information to answer the following questions. x bar = 30.1548 y bar = 1.0952 SS_xx = 19199.744 SS_yy = 1025.119 SS_xy = 2716.131 SSE = 640.876 Calculate a 90% confidence interval for the population mean weight change of baby snow geese who have a digestion efficiency of Round values in your final interval to 4 decimals, if

Explanation / Answer

Here I assume SSxx is var(x), SSyy is var(y) and SSxy is cov(x,y) If these are other values then change following accordingly

Slope=Covariance(X,Y)/Var(X) = 2716.131/19199.744=0.14

Intercept=Ybar-slope*xbar=1.0952-0.14*20.1548 =-1.73

Regression equation is Y= -1.73 +0.14 *X

Hence For 20% digestive efficiency predicted weight change yhat=-1.73+0.14*20 =1.07%

Degree of freedom=n-2=42-2=40

Critical t for 90% confidence interval t(0.10,40)=1.684

90% confidence interval =yhat± t(0.1,40)*sqrt(MSE)*sqrt(1+1/n+(x0-xbar)2/(n-1)*Sxx)

=1.07±1.684*sqrt(640.876/40)*sqrt(1+1/42+(20-30.1548)2/(42-1)*19199.744)

=(-5.7508        7.8908)

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