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# HW1 - Question 10(a The scatter plot of brain weight versu...

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0 2000 4000 6000 Brain_weight 0 2000 4000 6000 8000 Body_Weight -2 0 2 4 6 8 LOG_Brain_WT -5 0 5 10 LOG_Body_WT Question 10: (a) The scatter plot of brain weight versu body weight. From the scatter plot, we can hardly see any obvious relationshop between them. (b) The scatter plot of log(brain weight) versus log(body weight). We can see obvious linear relationship between them.

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(c) The model for the regression is: = + + LogBrainWeight β0 β1LogBodyWeight ε The result is : ----------------------------------------------------------------------------------------------- | Coefficient Std. Err. t P Value [95% Conf. Interval] -------+--------------------------------------------------------------------------------------- β1 | 1.221642 .0463011 26.38 0.000 1.129026 1.314258 β0 | -2.495622 .183841 -13.57 0.000 -2.863359 -2.127885 R Square = 0.9207, which means 92.07% percentage of variation in the response is explained by the model. (d) The expected average Log(brain weight) when Body Weith = 250Kg is : -2.495622 + 1.221642 * log(250) = 4.2496 The standard error of this predicted values is : = . + +( . - . ) ( - . ) 0 78681 162 1 3375 5 5215 2162 Xi 1 3375 2 = 0.9070 The 95% confidence interval is: . , . * . 4 2496 t60 0 025 0 9070 = (2.4356, 6.0636)
Question 14: (a) From the scatter plots, the relationship between Y and Xs are not so obvious, although we can see positive relationship between y and X4, negative relationship between Y and X1, X2.

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