UCLA STATS 101A - stats_101a_hw2 (14 pages)

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stats_101a_hw2



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stats_101a_hw2

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Pages:
14
School:
University of California, Los Angeles
Course:
Stats 101a - Introduction to Design and Analysis of Experiment
Introduction to Design and Analysis of Experiment Documents

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Stats 101a Hw 2 Linda Che 404449070 Section 1A 10 24 2017 Problem 1 a In the conclusion it was stated 99 4 of variability is du to calculating the sum of the residuals This contradicts the plot of residuals where there are some points far from the center indicating there are leverage points and outliers The residual plot shows a pattern and is not completely randomized b The traditional linear model does seem to fit it well except the residual plot seems to have a pattern You can improve it by getting rid of a leverage point and outliers Getting rid of the outliers would make the x a better predictor value and would improve the R 2 It would also randomize the residuals so that the residual plot doesn t violate the linear model Problem 2 library alr3 Loading required package car library car diamonds read table Downloads diamonds txt header TRUE part 1 a m2 lm Size Price diamonds summary m2 Call lm formula Size Price data diamonds Residuals Min 1Q Median 3Q Max 0 019873 0 005567 0 000120 0 005478 0 022062 Coefficients Estimate Std Error t value Pr t Intercept 0 0723394 0 0030740 23 53 2e 16 Price 0 0002634 0 0000057 46 20 2e 16 Signif codes 0 0 001 0 01 0 05 0 1 1 Residual standard error 0 008414 on 47 degrees of freedom Multiple R squared 0 9785 Adjusted R squared 0 978 F statistic 2135 on 1 and 47 DF p value 2 2e 16 plot diamonds Price diamonds Size abline m2 par mfrow c 2 2 plot m2 b The linear model seems to fit the plot pretty well and there seems to be a linear relationship between the size and price of diamonds However if you look closely at the residual plot you can see that there is a pattern which would be a violation of the traditional linear fit Part 2 a summary powerTransform cbind diamonds Size diamonds Price 1 data diamonds bcPower Transformations to Multinormality Est Power Rounded Pwr Wald Lwr bnd Wald Upr Bnd Y1 0 2393 0 1 0400 0 5615 Y2 0 0172 0 0 6114 0 5771 Likelihood ratio tests about transformation parameters LRT df pval LR test lambda 0 0 1



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