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BIO503: Tutorial 3 Solutions

BIO503: Tutorial 3 Solutions. Harvard School of Public Health Wintersession 2009. Solar Radiation Data. 1A. Assign the data to an object called solar.radiation. > solar.radiation <- c(11.1, 10.6, 6.3, 8.8, 10.7, 11.2, 8.9, 12.2)

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BIO503: Tutorial 3 Solutions

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  1. BIO503: Tutorial 3 Solutions Harvard School of Public Health Wintersession 2009

  2. Solar Radiation Data 1A. Assign the data to an object called solar.radiation. > solar.radiation <- c(11.1, 10.6, 6.3, 8.8, 10.7, 11.2, 8.9, 12.2) 1B. Find the mean, median, and variance of the radiation observations. > mean(solar.radiation) > median(solar.radiation) > variance(solar.radiation)

  3. 1C. Add 10 to solar.radiation > sr10 <- solar.radiation + 10 Find the mean, median, variance of sr10. > mean(sr10) > median(sr10) > variance(sr10) The mean and median values change but the variance remains the same as that for the solar.radiation data.

  4. 1D. Multiple solar.radiation by -2 1D. Multiply each observation by -2: > srm2 <- solar.radiation*(-2) > mean(srm2) > median(srm2) > variance(srm2) The mean, median and variance values of srm2 are different from those for solar.radiation.

  5. 1E. Histograms Plot of histogram of solar.radiation, sr10 and srm2. > win.graph(32,16) > par(mfrow=c(1,3)) > hist(solar.radiation, main="solar.radiation", col="blue") > hist(sr10, main="sr10", col="gold") > hist(srm2, main="srm2", col="purple")

  6. 1F. Make a scatter plot > plot(solar.radiation, ylab="solar radiation observed", main="solar radiation data for tutorial 3") > date <- 1:8 > lmObj <- lm(solar.radiation ~ date)

  7. 1G. Add a fitted line > plot(date, solar.radiation, ylab="solar radiation observed", xlab="date", main="solar radiation data for tutorial 3") > abline(lmObj, lwd=3, col="green", lty=2)

  8. 1H. Which variance formula? Compute each of the quantities: The first formula: > n <- length(solar.radiation) > formula1 <- (1/n)*sum((solar.radiation - mean(solar.radiation))^2) The second formula: > formula2 <- (1/(n-1))*sum((solar.radiation - mean(solar.radiation))^2) > var(solar.radiation) == formula1 > var(solar.radiation) == formula2 R uses the sample variance (formula2) formula for the var function.

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