Question

R programming

R1. Below is a table showing a variety of countries (first column), the number of cigarettes consumed per adult per year (second column), and the rate at which people die from coronary heart disease CHD) per 100,000 people (third column). Put these data into a dataframe in R. Then run a linear regression that examines how CHD rates (response variable) are predicted by cigarette consumption (predictor variable). What is the equation of the regression line you get? What are the units on the slope? Interpret the slope in this context. [Include your code, equation, units, and slope interpretation.] United States Canada Australia New Zealand United Kingdom Switzerland reland Iceland Finland West Germany 3900 3350 3220 256.9 211.6 238.1 211.8 194. 2790 187.3 110.5 233.1 150.3 124.7 41.2 82.1 118.1 31.9 14.3 144.9 59.7 126.9 43.9 36.3 2290 2160 1890 Netherlands 1800 1770 1700 1680 1510 1500 Austria Belgium Mexico Italy Denmark France Sweden 1270 1200 1090 Norway R2. Figure out how to use the output from the Im function to create a residual plot, and then use this to help as you discuss each of the conditions required for building a linear model and whether you think they are met. R3. In Mauritania, the annual cigarette consumption is 30.3 cigarettes per peon. Predict the CHD rate using your model, ande look up this result on the interet. Discuss what you find and why it might be happening.

Answer 1

Importing rawdata rawdata <- read.csv ("rawdata.csv", stringsAsFactors-, headerT) head (rawdata) ## cigarettes . consumed CHD ## 1 3900 256.9 ## 2 3350 211.6 ## 3 3220 238.1 ## 4 3220 211.8 ## 5 2790 194.1 t 6 2780 1243.0 regression model model <- lm (CHD~Cigarettes.consumed, datarawdata) summary (model) ## Call: ## 1m (formula = CHD ~ Cigarettes.consumed, data- rawdata) ## Residuals: Min 1Q Median ## 3 Max -445.1-287.8-178.5-108.0 1371.7 Coefficients: Estimate Std. Error t value Pr(>ItI) ## (Intercept) 9.2842 333.51740.028 0.978 0.1776 0.1459 1.218 0.238 ## Cigarettes . consumed # Residual standard error: 531.1 on 19 degrees of freedom Multiple 0.07238, Adjusted R-squared 0.02356 ## R-squared: ## F-statistic: 1.483 on 1 and 19 DF, p-value : 0.2383

Regression equation CHD = 9.2842 + 0.1776 Cigarettes-consumed One unit increased in the cigarettes consumed, the CHD increases by 9.2842 units Unit of the slope of CDH per 100000 people/number of cig. consumed by an adult per year Residual Analysis par (mfrow弌(2,2)) plot (model) Residuals vs Fitted Normal Q-Q 70 7o 010 010 o 6c o 06 200 300 400 500 600 700 Fitted values Theoretical Quantiles Scale-Location Residuals vs Leverage 010 010 0.5 200 300 400 500 600 700 0.00 0.05 0.10 0.15 0.20 0.25 Fitted values Leverage

Residuals vs Fitted Plot Residual plots are used to look for underlying patterns in the residuals that may mean that the model has a problem. In plot.we see a obvious distinct pattern, indication the model is not good Normal Q-Q (quantile-quantile) Plot Residuals should be normally distributed and the Q-Q Plot will show this. If residuals follow close to a straight line on this plot, it is a good indication they are normally distributed. From the plot we see the points are not nicely aligned along the normal line, indicating that the residuals not are normal distributed Scale-Location This plot test the linear regression assumption of equal variance (homoscedasticity) i.e. that the residuals have equal variance along the regression line In the plot above we see the residuals are not spread out in a random manner indicating hetroscedasticity Residuals vs Leverage This plot can be used to find influential cases in the dataset. An influential case is one that, if removed, will affect the model so its inclusion or exclusion should be considered. An influential case will appear in the top right or bottom left of the chart inside a red line which marks Cook's Distance In the above plot we see not point is beyond the Cook's distance.