hw5_solutions

hw5_solutions - STAT 3022 Lab, March 30, 2009 TA: Jinghan...

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Unformatted text preview: STAT 3022 Lab, March 30, 2009 TA: Jinghan Meng EX 10.10 (a) > tuition <- read.table("E:/DataSets/PC-Text/ch10/ta10_001.txt", + sep="\t",header=T) > attach(tuition) > plot(Year.2000, Year.2005, main="Tuition 2000 versus 2005") 3000 4000 5000 6000 7000 4000 6000 8000 10000 Tuition 2000 versus 2005 Year2000 Year2005 The plot shows a strong linear relationship with no striking outliers. (b) > m <- lm(Year.2005 ~ Year.2000) > summary(m) Call: lm(formula = Year.2005 ~ Year.2000) Residuals: Min 1Q Median 3Q Max-1559.04-341.78 47.53 568.54 932.99 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 1.059e+03 3.968e+02 2.669 0.0122 * Year.2000 1.393e+00 8.988e-02 15.498 7.34e-16 *** Residual standard error: 626.6 on 30 degrees of freedom Multiple R-squared: 0.889, Adjusted R-squared: 0.8853 F-statistic: 240.2 on 1 and 30 DF, p-value: 7.337e-16 1 STAT 3022 Lab, March 30, 2009 TA: Jinghan Meng The regression line is ˆ y = 1059 + 1 . 393 x . (c) > plot(Year.2000, residuals(m), main="Residuals versus 2000") > abline(h=0) > hist(residuals(m)) In the plot (below, left), it appears that large x values, many residuals are negative. 3000 4000 5000 6000 7000-1500-1000-500 500 1000 Residuals versus 2000 Year2000 residuals(m) Histogram of residuals(m) residuals(m) Frequency-2000-1500-1000-500 500 1000 2 4 6 8 (d) The histogram (above, right) suggests a left skew. (e) To test for a relationship, we test H : β 1 = 0 vs. H a : β 1 6 = 0. (f) From the above R output, the test statistic t = 15 . 498 with df = 30, and p-value is 7.34e-16. We have strong evidence of a non-zero slope. EX 10.11 (a) From the above R output, the estimate of β 1 is 1.393, standard error is 8.988e-02. For the 95% confidence interval, t * is > qt(0.975,30) [1] 2.042272 So 95% is 1 . 393 ± 2 . 042272 × . 08988 = [1 . 2095 , 1 . 5765]. When tuition in 2000 is $5000, the predicted tuition in 2005 is 8024.048. The 95% confidence interval is [7758 . 128 , 8289 . 969]. This slope means that a $1 difference in tuition in 2000 changes 2005 tuition by between $1.21 and $1.58, so we estimate that tuition increase by 21% and 58%. (b) When x = 5000, the estimated 2005 tuition is ˆ y = 1059+1 . 393(5000) = 8024 . 048....
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This note was uploaded on 02/24/2011 for the course STAT 3022 taught by Professor Staff during the Spring '08 term at Minnesota.

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hw5_solutions - STAT 3022 Lab, March 30, 2009 TA: Jinghan...

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