Please Use R program! City MORT PRECIP EDUC NONWHITE NOX SO2 San Jose, CA 790.73

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Please Use R program!

City MORT PRECIP EDUC NONWHITE NOX SO2 San Jose, CA 790.73 13 12.2 3 32 3 Wichita, KS 823.76 28 12.1 7.5 2 1 San Diego, CA 839.71 10 12.1 5.9 66 20 Lancaster, PA 844.05 43 9.5 2.9 7 32 Minneapolis, MN 857.62 25 12.1 3 11 26 Dallas, TX 860.1 35 11.8 14.8 1 1 Miami, FL 861.44 60 11.5 11.5 1 1 Los Angeles, CA 861.83 11 12.1 7.8 319 130 Grand Rapids, MI 871.34 31 10.9 5.1 3 10 Denver, CO 871.77 15 12.2 4.7 8 28 Rochester, NY 874.28 32 11.1 5 4 18 Hartford, CT 887.47 43 11.5 7.2 3 10 Fort Worth, TX 891.71 31 11.4 11.5 1 1 Portland, OR 893.99 37 12 3.6 21 44 Worcester, MA 895.7 45 11.1 1 3 8 Seattle, WA 899.26 35 12.2 5.7 7 20 Bridgeport, CT 899.53 45 10.6 5.3 4 4 Springfield, MA 904.16 45 11.1 3.4 4 20 San Francisco, CA 911.7 18 12.2 13.7 171 86 York, PA 911.82 42 9 4.8 8 49 Utica, NY 912.2 40 10.3 2.5 2 11 Canton, OH 912.35 36 10.7 6.7 7 20 Kansas City, MO 919.73 35 12 12.6 4 4 Akron, OH 921.87 36 11.4 8.8 15 59 New Haven, CT 923.23 46 11.3 8.8 3 8 Milwaukee, WI 929.15 30 11.1 5.8 23 125 Boston, MA 934.7 43 12.1 3.5 32 62 Dayton, OH 936.23 36 11.4 12.4 4 16 Providence, RI 938.5 42 10.1 2.2 4 18 Flint, MI 941.18 30 10.8 13.1 4 11 Reading, PA 946.18 41 9.6 2.7 11 89 Syracuse, NY 950.67 38 11.4 3.8 5 25 Houston, TX 952.53 46 11.4 21 5 1 Saint Louis, MO 953.56 34 9.7 17.2 15 68 Youngstown, OH 954.44 38 10.7 11.7 13 39 Columbus, OH 958.84 37 11.9 13.1 9 15 Detroit, MI 959.22 31 10.8 15.8 35 124 Nashville, TN 961.01 45 10.1 21 14 78 Allentown, PA 962.35 44 9.8 0.8 6 33 Washington, D.C. 967.8 41 12.3 25.9 38 102 Indianapolis, IN 968.66 39 11.4 15.6 7 33 Cincinnati, OH 970.47 40 10.2 13 26 146 Greensboro, NC 971.12 42 10.4 22.7 3 5 Toledo, OH 972.46 31 10.7 9.5 7 25 Atlanta, GA 982.29 47 11.1 27.1 8 24 Cleveland, OH 985.95 35 11.1 14.7 21 64 Louisville,KY 989.27 30 9.9 13.1 37 193 Pittsburg, PA 991.29 36 10.6 8.1 59 263 New York, NY 994.65 42 10.7 11.3 26 108 Albany, NY 997.88 35 11 3.5 10 39 Buffalo, NY 1001.9 36 10.5 8.1 12 37 Wilmington, DE 1003.5 45 11.3 12.1 11 42 Memphis, TN 1006.49 50 10.4 36.7 18 34 Philadelphia, PA 1015.02 42 10.5 17.5 32 161 Chattanooga, TN 1017.61 52 9.6 22.2 8 27 Chicago, IL 1024.89 33 10.9 16.3 63 278 Richmond, VA 1025.5 44 11 28.6 9 48 Birmingham, AL 1030.38 53 10.2 38.5 32 72 Baltimore, MD 1071.29 43 9.6 24.4 38 206 New Orleans, LA 1113.06 54 9.7 31.4 17 1 McDonald and Ayers [1978] present data from an early study that examined the possible link between air pollution and mortality. Table B.15 summarizes the data. The response MORT is the total age-adjusted mortality from all

Explanation / Answer

a) Full model fits the data better as opposed to a reduced model. The same can be verified by looking at the value of adjusted R sq.

For full model, value is 64.44% , whereas for reduced model it is 46.59%.

FOR REDUCED MODEL

Coefficients:

Estimate Std. Error t value Pr(>|t|)   

(Intercept) 784.604724 27.757550 28.266 < 2e-16 ***

SO2 0.478689 0.103157 4.640 2.14e-05 ***

PRECIP 3.483581 0.682695 5.103 4.14e-06 ***

NOX -0.006816 0.160391 -0.042 0.966   

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 45.46 on 56 degrees of freedom

Multiple R-squared: 0.4931, Adjusted R-squared: 0.4659

F-statistic: 18.16 on 3 and 56 DF, p-value: 2.366e-08

For FULL MODEL

Coefficients:

Estimate Std. Error t value Pr(>|t|)   

(Intercept) 995.63646 91.64099 10.865 3.35e-15 ***

SO2 0.35518 0.09096 3.905 0.000264 ***

PRECIP 1.40734 0.68914 2.042 0.046032 *  

NOX -0.10797 0.13502 -0.800 0.427426   

NONWHITE 3.19909 0.62231 5.141 3.89e-06 ***

EDUC -14.80139 7.02747 -2.106 0.039849 *  

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 37.09 on 54 degrees of freedom

Multiple R-squared: 0.6746, Adjusted R-squared: 0.6444

F-statistic: 22.39 on 5 and 54 DF, p-value: 4.407e-12

b) Looking at the Full model response and checking the values of EDUC & NONWHITE

For NONWHITE we can refer a t-value of 5.141 and a p-value of 3.89e-06 making it very significant.

Similarly, for EDUC we can refer a t-value of -2.106 and a p-value of 0.03 making it significant.

Above values are calculated based on sum of squares approach.

In addition, an ANOVA analysis too can be conducted to check the following

summary(aov(formula = MORT~EDUC+NONWHITE+EDUC*NONWHITE,data=Mort))
Df Sum Sq Mean Sq F value Pr(>F)   
EDUC 1 59604 59604 33.805 3.04e-07 ***
NONWHITE 1 69778 69778 39.575 5.09e-08 ***
EDUC:NONWHITE 1 157 157 0.089 0.767   
Residuals 56 98737 1763

c) Plotting the graph of b/w MORT & EDUC and MORT & NONWHITE we can see both the graphs share linear relationship with MORT.

Based on above, researchers would like to infer that more the NONWHITE pecent the more the Mortality rate.

Reseachers might want to see the behaviour of working conditions i.e. How mortality is getting impacted by the air pollution in the working conditions and variables such as education and nonwhite help researchers with some valueable insight.

Note :

Linear Model was run to identify the key important variables and thier relationship with Mortality.

Model prepared is not the best fit model and can be improvised further by removing outliers and data transformation.

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