Homework03Solns - Stat 512 2 Solutions to Homework #3 Dr....

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Stat 512 – 2 Solutions to Homework #3 Dr. Simonsen Due Wednesday, September 14, 2005. For the next 3 questions use the grade point average data described in the text with KNNL problem 1.19. 1. Describe the distribution of the explanatory variable. Show the plots and output that were helpful in learning about this variable. [Note to grader: this is an open-ended question. As long as there is a good description, they do not have to have exactly the same results as in these solutions.] Using PROC UNIVARIATE we see there are 120 observations ranging between 14 and 35 with a mean of 24.725 and median of 25; their standard deviation is 4.472. There do not appear to be any extreme observations (i.e., ones far away from the others) in the histogram plot below. An examination of the boxplot, histogram, and qqplot (not all of these are necessary) shows that the distribution of the test scores appears to be reasonably symmetric and approximately normal. The UNIVARIATE Procedure Variable: testscore Moments N 120 Sum Weights 120 Mean 24.725 Sum Observations 2967 Std Deviation 4.47206549 Variance 19.9993697 Skewness -0.1363553 Kurtosis -0.5596968 Uncorrected SS 75739 Corrected SS 2379.925 Coeff Variation 18.0872214 Std Error Mean 0.40824186 Basic Statistical Measures Location Variability Mean 24.72500 Std Deviation 4.47207 Median 25.00000 Variance 19.99937 Mode 24.00000 Range 21.00000 Interquartile Range 7.00000 Extreme Observations ----Lowest---- ----Highest--- Value Obs Value Obs 14 2 32 84 15 48 32 104 16 119 33 15 16 52 34 80 16 32 35 106 Stem Leaf # Boxplot 35 0 1 | 34 0 1 | 33 0 1 | 32 0000 4 | 31 0000 4 | 30 0000000 7 | 29 0000000 7 | 28 0000000000 10 +-----+ 27 0000000000 10 | | 26 0000000000 10 | | 25 0000000000 10 *-----* 24 000000000000 12 | + | 23 00000 5 | |
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22 0000 4 | | 21 000000000 9 +-----+ 20 0000000000 10 | 19 000 3 | 18 0000000 7 | 17 | 16 000 3 | 15 0 1 | 14 0 1 | ----+----+----+----+ 2. Run the linear regression to predict GPA from the entrance test score and obtain the residuals (do not include a list of the residuals in your solution). (a) Verify that the sum of the residuals is zero by running PROC UNIVARIATE with the output from the regression. The UNIVARIATE Procedure Variable: resid (Residual) Moments N 120 Sum Weights 120 Mean 0 Sum Observations 0 Std Deviation 0.62050134 Variance 0.38502191 Skewness -1.0067279 Kurtosis 2.50187662 Uncorrected SS 45.8176078 Corrected SS 45.8176078 Coeff Variation . Std Error Mean 0.05664376
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(b) Plot the residuals versus the explanatory variable and briefly describe the plot noting any unusual patterns or points. There does not appear to be any obvious pattern in this residual plot. It looks like a random scatter of points and the variance is reasonably constant. There is one potential outlier with test score = 29 which appears to have an unusually low residual: this is observation 9 with testscore=29 (above average) and gpa = 0.5, which is strangely low. (c) Plot the residuals versus the order in which the data appear in the data file and briefly describe the plot noting any unusual patterns or points.
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There is no obvious pattern of residuals in the order they appear in the file. The potential outlier (observation 9) appears again. [Note to grader: a regression or smoothed line is also fine on this plot.] (d) Examine the distribution of the residuals by getting a histogram and a normal probability plot of the residuals by using the histogram and qqplot statements in PROC UNIVARIATE . What do you conclude?
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This note was uploaded on 02/02/2012 for the course STAT stat512 taught by Professor Libo during the Spring '11 term at Purdue North Central.

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Homework03Solns - Stat 512 2 Solutions to Homework #3 Dr....

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