# Introductory Statistics - STAT670

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STAT670

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StatisticsStudent Name:Student ID:Course:Date: 1stNovember 2017

Report 1IntroductionA study was undertaken to investigate whether death rates could be predicted from factorsrelated to air pollution, weather and/or socioeconomic variables. In this report we present theresults of the regression analysis that was conducted.MethodsRegression analysis model was conducted to predict death rate from each of the 6 potentialpredictors (Average annual precipitation, Average January maximum temperature, Average Julymaximum temperature, Average household size (number of people in a household),Percentagewhite population in urbanized areas andRelative sulphur dioxide pollution potential in 1960).Analysis of data was done using Minitab. Six different regression models were performed. Thedata filecontained data recorded on a random sample of 60 metropolitan areas in the USA. Eachmetropolitan area contains information from the late 1950s-early 1960s recorded on the each ofthe variables described below.ResultsAs mentioned in the methodology, six different regression models were performed.Table1: Regression modelsModelIndependent VariableR-SquaredCoefficientP-valueModel 1Average annual precipitation26.0%3.170.000Model 2AverageJanuarymaximumtemperature0.3%-0.300.660Model 3AverageJulymaximumtemperature7.8%3.630.031

Model 4Average household size12.8%164.340.005Model 5Percentagewhitepopulationinurbanized areas41.4%-4.490.000Model 6Relative sulphur dioxidepollution potential in 196018.1%0.420.001Ascanbeseenfromtable1,itisonlymodel2(independentvariablebeing“AverageJanuarymaximum temperature”) that was found to be insignificance (p-value > 0.05). The rest of the othermodels were significant.The best predictor of mortality is the “Percentagewhitepopulationin urbanized areas”, this isbased on the fact that it explains a large proportion of variation (41.4%) in the dependentvariable (mortality).Interpretation of the coefficients for the significant predictorsThe coefficient of theAverage annual precipitation is 3.17; this suggests that a unitincrease in the Average annual precipitation would result to an increase in the mortalityby 3.17. Similarly, a unit decrease in the Average annual precipitation would result to adecrease in the mortality by 3.17.The coefficient of theAverageJulymaximum temperature is 3.63; this suggests that aunit increase in the AverageJulymaximum temperature would result to an increase in themortality by 3.63. Similarly, a unit decrease in the AverageJulymaximum temperaturewould result to a decrease in the mortality by 3.63.The coefficient of theAverage household size is 164.34; this suggests that a unit increasein the Average household size would result to an increase in the mortality by 164.34.Similarly, a unit decrease in the Average household size would result to a decrease in themortality by 164.34.

The coefficient of the Percentagewhitepopulationin urbanized areasis -4.49; thissuggests that a unit increase in thePercentagewhitepopulationin urbanized areaswouldresult to a decrease in the mortality by 4.49. Similarly, a unit decrease in thePercentagewhitepopulationin urbanized areaswould result to an increase in themortality by 4.49.The coefficient of theRelative sulphur dioxide pollution potential in 1960 is 0.42; thissuggests that a unit increase in the Relative sulphur dioxide pollution potential in 1960would result to an increase in the mortality by 0.42. Similarly, a unit decrease in theRelative sulphur dioxide pollution potential in 1960 would result to a decrease in themortality by 0.42.ConclusionThis study sought to predict the mortality using the different predictors. Results showed that 5out 6 predictors were significant in the model.AverageJanuarymaximum temperature wasfound to be insignificant in the model (p-value > 0.05).The best predictor of mortality is the“Percentagewhitepopulationin urbanized areas”, this is based on the fact that it explains a largeproportion of variation (41.4%) in the dependent variable (mortality).AppendixModel 1:Regression Analysis: Mort versus PrecipThe regression equation isMort = 822 + 3.17 Precip

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