City MORT PRECIP EDUC NONWHITE NOX SO2 San Jose, CA 790.73 13 12.2 3 32 3 Wichit

Question

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

Full Model Stats :

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

Highlighted above are the overall F-stat and the p-value which states the regression is highly significant and hence the null hypothesis can be rejected. '

b)

predict(Model01,newdata,interval="confidence")
fit lwr upr
889.4458 837.6935 941.1981

c) Extrapolating for Cooleyville happened from the linear regression equation created above.

We should not be concerned as the data points of cooleyville lies within permissible limits of what we have worked on , though as word of caution, since in our model we have not carried out data transformation and outlier handling the permissible limits or extrapolated values might not reflect the true/exact predict (which couldbe worrisome).

d)

Covariance Matrix

vcov(Model01)
(Intercept) SO2 PRECIP NOX NONWHITE EDUC
(Intercept) 8398.07154211 -3.028709353 -38.389563447 0.031394638 4.989930752 -623.1172079
SO2 -3.02870935 0.008273768 0.006866429 -0.004868993 -0.007432491 0.2302377
PRECIP -38.38956345 0.006866429 0.474918283 0.038450139 -0.188657411 1.9714320
NOX 0.03139464 -0.004868993 0.038450139 0.018231423 -0.016767545 -0.1297316
NONWHITE 4.98993075 -0.007432491 -0.188657411 -0.016767545 0.387267925 -0.1593543
EDUC -623.11720792 0.230237682 1.971431996 -0.129731559 -0.159354335 49.3852832

Covariance to Correlation

cov2cor(vcov(Model01))
(Intercept) SO2 PRECIP NOX NONWHITE EDUC
(Intercept) 1.000000000 -0.3633424 -0.6078745 0.002537204 0.08749817 -0.9675673
SO2 -0.363342442 1.0000000 0.1095393 -0.396439752 -0.13130369 0.3601853
PRECIP -0.607874526 0.1095393 1.0000000 0.413217013 -0.43990476 0.4070742
NOX 0.002537204 -0.3964398 0.4132170 1.000000000 -0.19955078 -0.1367214
NONWHITE 0.087498170 -0.1313037 -0.4399048 -0.199550781 1.00000000 -0.0364384
EDUC -0.967567306 0.3601853 0.4070742 -0.136721428 -0.03643840 1.0000000

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