Problem 1 (questions 3-11). USE R CODE TO PROVIDE ANSWERS TO THE…

QuestionProblem 1 (questions 3-11). USE R CODE TO PROVIDE ANSWERS TO THE…Problem 1 (questions 3-11) . USE R CODE TO PROVIDE ANSWERS TO THE FOLLWOING QUESTIONS. ALSO PRESENT R CODE AND SCREEN SHOT OF THE RESULTSUsing this dataset Pollution.xlsx that contains 15 variables for 60 cities. The variables included in this file are: Response ~ Mortality: Total age-adjusted mortality from all causes, in deaths per 100,000 population mean annual precipitation (in inches);percent relative humidity (annual average at 1 P.M.);mean January temperature (in degrees Fahrenheit);mean July temperature (in degrees Fahrenheit);percentage of the population aged 65 years or over;population per household;median number of school years completed by persons of age 25 years or more;percentage of the housing that is sound with all facilities;population density (in persons per square mile of urbanized area);percentage of 1960 population that is nonwhite;percentage of employment in white-collar occupations;percentage of households with annual income under $3,000 in 1960;relative pollution potential of hydrocarbons (HC);relative pollution potential of oxides of nitrogen (NOX ); andrelative pollution potential of sulphur dioxide (SO2). Note: This data has problems with influential observations and with lack of independence due to spatial correlation; ignore these issues while solving this exercise. We want to determine whether the pollution variables (13, 14, and 15) are associated with mortality, after the other climate and socioeconomic variables are accounted for.With mortality as the response, calculate Cp values and select the best fitting regression model involving weather and socioeconomic variables as explanatory variables (do not include variables 13,14 and 15 yet). Report the Cp of the model you selected.   This is Model1. 1.Report the model you selected based on the Cp value. Answer TRUE if the explanatory variable was included in the Model, and FALSE if the variable was not part of the model. mean annual precipitation (in inches);________percent relative humidity (annual average at 1 P.M.);________mean January temperature (in degrees Fahrenheit);________mean July temperature (in degrees Fahrenheit);________percentage of the population aged 65 years or over;________population per household;________median number of school years completed by persons of age 25 years or more;________percentage of the housing that is sound with all facilities;________population density (in persons per square mile of urbanized area);________percentage of 1960 population that is nonwhite;________percentage of employment in white-collar occupations;________percentage of households with annual income under $3,000 in 1960________2. To the model with the lowest AIC (Model1), add the three pollution variables (variables 13, 14 and 15, transformed to their logarithms) and obtain the p-value from the extra-sum-of-squares F-test due to their addition. ________3. Are the pollution variables (13,14 and 15) joinly statistically significant in this model?  Yes/No________4. With mortality as the response, use Forward selection (AIC) to find the best fitting regression model involving weather and socioeconomic variables as explanatory variables (do not include variables 13,14 and 15 yet). Report the AIC of the model you selected________. This is Model25. Report the model you selected based on the AIC value. Answer TRUE if the explanatory variable was included in the Model, and FALSE if the variable was not part of the model. mean annual precipitation (in inches);________percent relative humidity (annual average at 1 P.M.);________mean January temperature (in degrees Fahrenheit);________mean July temperature (in degrees Fahrenheit);________percentage of the population aged 65 years or over;________population per household;________median number of school years completed by persons of age 25 years or more;________percentage of the housing that is sound with all facilities;________population density (in persons per square mile of urbanized area);________percentage of 1960 population that is nonwhite;________percentage of employment in white-collar occupations;________percentage of households with annual income under $3,000 in 1960;________ Use backward elimination selection technique in this problem (include variables 1-12) and report the AIC value of your selected model. This is Model3 Report the model you selected based on the AIC value for backward selection. Answer TRUE if the explanatory variable was included in the Model, and FALSE if the variable was not part of the model. mean annual precipitation (in inches);_______percent relative humidity (annual average at 1 P.M.);_______mean January temperature (in degrees Fahrenheit);_______mean July temperature (in degrees Fahrenheit);_______percentage of the population aged 65 years or over;_______population per household;_______median number of school years completed by persons of age 25 years or more;_______percentage of the housing that is sound with all facilities;_______population density (in persons per square mile of urbanized area);_______percentage of 1960 population that is nonwhite;_______percentage of employment in white-collar occupations;_______percentage of households with annual income under $3,000 in 1960_______Run Model2 and Model3 with added pollution variables (13,14,15 in their log form).  Compare your results with Model1+pollution variables and report the highest Adjusted R-squared across these models.  _______ Did you arrive to the same set of variables using backward and forward selection techniques? Yes/No _______ CITY Mortality Precip Humidity JanTemp JulyTemp Over65 House Educ Sound Density NonWhite WhiteCol Poor HC NOX SO2San Jose, CA 925,73 13 71 49 68 7 3,36 13,5 90,7 2702 3 51,9 9,7 105 32 3Wichita, KS 958,76 28 54 32 81 7 3,27 13,2 81 3665 7,5 51,6 13,2 4 2 1San Diego, CA 974,71 10 61 55 70 7,3 3,11 12,1 88,9 3033 5,9 51 14 144 66 20Lancaster, PA 979,05 43 54 32 74 10,1 3,38 11,7 79,2 3214 2,9 43,7 12 11 7 32Minneapolis, MN 992,62 25 58 12 73 9,2 3,28 12,1 83,1 2095 2 51,9 9,8 20 11 26Dallas, TX 995,1 35 54 46 85 7,1 3,22 11,8 79,9 1441 14,8 51,2 16,1 1 1 1Miami, FL 996,44 60 60 67 82 10 2,98 11,5 88,6 4657 13,5 47,3 22,4 3 1 1Los Angeles, CA 996,83 11 47 53 68 9,2 2,99 12,1 90,6 4700 7,8 48,9 12,3 648 319 130Grand Rapids, MI 1006,34 31 61 24 72 9 3,37 12,7 82,8 3226 5,1 45,2 12,3 5 3 10Denver, CO 1006,77 15 38 30 73 8,2 3,15 12,2 84,2 4824 4,7 53,1 12,7 17 8 28Rochester, NY 1009,28 32 60 25 72 10,9 3,21 11,1 82,5 4355 5 46,4 10,8 7 4 18Hartford, CT 1022,47 43 56 27 72 9 3,25 11,5 87,1 2909 7,2 51,6 9,5 7 3 10Fort Worth, TX 1026,71 31 53 45 85 7,3 3,22 11,4 80,7 1844 11,5 48,1 18,5 1 1 1Portland, OR 1028,99 37 73 38 67 11,3 2,99 12 81,5 3387 3,6 50,3 13,5 56 21 44Worcester, MA 1030,7 45 56 24 70 11,8 3,25 11,1 79,8 3678 1 44,8 14 7 3 8Seattle, WA 1034,26 35 72 40 64 9,6 3,02 12,2 82,5 3626 5,7 54,3 10,1 20 7 20Bridgeport, CT 1034,53 45 56 30 73 9,3 3,29 10,6 86 2140 5,3 40,4 10,5 6 4 4Springfield, MA 1039,16 45 56 28 74 10,6 3,21 11,1 82,6 1883 3,4 41,9 12,3 5 4 20San Francisco, CA 1046,7 18 71 48 63 9,2 2,92 12,2 87,7 4253 13,7 51,2 12 311 171 86York, PA 1046,82 42 54 33 76 9,7 3,22 13,1 76,2 9699 4,8 42,2 14,5 8 8 49Utica, NY 1047,2 40 60 23 71 11,3 3,28 10,3 73,8 1671 2,5 47,4 13,5 5 2 11Canton, OH 1047,35 36 59 27 72 9,5 3,36 10,7 79,3 4213 6,7 41 13,2 12 7 20Kansas City, MO 1054,73 35 55 31 81 9,2 3,1 12 78,3 3262 12,6 48,6 13,9 7 4 4Akron, OH 1056,87 36 59 27 71 8,1 3,34 11,4 81,5 3243 8,8 42,6 11,7 21 15 59New Haven, CT 1058,23 46 58 30 72 10,2 3,16 11,3 83,2 3327 8,8 45,3 12,2 4 3 8Milwaukee, WI 1064,15 30 64 20 69 8,8 3,26 11,1 85,4 2934 5,8 44 9,4 33 23 125Boston, MA 1069,7 43 56 30 74 10,9 3,23 12,1 83,9 4679 3,5 49,2 11,3 21 32 62Dayton, OH 1071,23 36 58 30 75 7,5 3,35 11,4 81,9 4029 12,4 44 12 6 4 16Providence, RI 1073,5 42 56 29 72 10,7 3,19 10,1 79,5 3508 2,2 38,8 15,7 6 4 18Flint, MI 1076,18 30 61 24 72 6,5 3,53 10,8 79,5 3694 13,1 33,8 12,4 11 4 11Reading, PA 1081,18 41 54 33 77 11,2 3,08 9,6 79,9 4843 2,7 38,6 14,1 11 11 89Syracuse, NY 1085,67 38 61 24 72 9,8 3,34 11,4 78 4923 3,8 50,5 11,1 8 5 25Houston, TX 1087,53 46 59 55 84 5,6 3,35 11,4 79,7 2647 21 46,9 17,9 6 5 1Saint Louis, MO 1088,56 34 57 32 79 9,3 3,23 9,7 76,8 5160 17,2 45,1 15,3 31 15 68Youngstown, OH 1089,44 38 58 28 72 8,9 3,48 10,7 79,8 3451 11,7 37,5 13 14 13 39Columbus, OH 1093,84 37 58 31 75 8 3,26 11,9 78,4 4259 13,1 49,6 13,9 23 9 15Detroit, MI 1094,22 31 59 27 74 7,2 3,44 10,8 87 4834 15,8 43,5 13,6 52 35 124Nashville, TN 1096,01 45 56 40 80 8,3 3,32 10,1 70,3 2682 21 46,1 24,1 17 14 78Allentown, PA 1097,35 44 54 29 74 10,4 3,21 9,8 81,6 4260 0,8 39,4 12,4 6 6 33Washington, DC 1102,8 41 52 37 78 6,2 3,25 12,3 89,5 5308 25,9 59,7 10,3 65 28 102Indianapolis, IN 1103,66 39 60 29 75 8,7 3,23 11,4 78,6 4412 15,6 46,6 13,2 13 7 33Cincinnati, OH 1105,47 40 57 34 77 9,2 3,21 10,2 77 4101 13 45,7 15,1 26 26 146Greeensboro, NC 1106,12 42 53 40 77 6,1 3,45 10,4 71,8 2269 22,7 41,4 19,5 8 3 5Toledo, OH 1107,46 31 59 26 73 9,3 3,22 10,7 81,3 3249 9,5 43,9 13,6 11 7 25Atlanta, GA 1117,29 47 56 45 79 6,5 3,41 11,1 77,5 3125 27,1 50,2 20,6 18 8 24Cleveland, OH 1120,95 35 60 28 71 8,8 3,29 11,1 86,3 3042 14,7 44,6 11,4 31 21 64Louisville, KY 1124,27 30 57 35 71 8,3 3,37 9,9 77,4 4474 13,1 42,6 17,7 38 37 193Pittsburgh, PA 1126,29 36 56 29 72 9,5 3,32 10,6 77,6 3437 8,1 45,5 13,8 45 59 263New York, NY 1129,65 42 58 33 77 9,7 3,03 10,7 83,5 7462 11,3 48,7 12,4 41 26 108Albany, NY 1132,88 35 57 23 72 11,1 3,14 11 78,8 4281 3,5 50,7 14,4 8 10 39Buffalo, NY 1136,9 36 61 24 70 9 3,31 10,5 83,2 6582 8,1 42,5 12,6 18 12 37Wilmington, DE 1138,5 45 56 33 76 7,7 3,39 11,3 82,2 3152 12,1 47,3 10,9 14 11 42Memphis, TN 1141,49 50 59 42 82 7,3 3,49 10,4 72,5 3497 36,7 43,3 26,4 15 18 34Philadelphia, PA 1150,02 42 54 32 76 9,1 3,32 10,5 87,5 6092 17,5 45,3 13,2 29 32 161Chattanooga, TN 1152,61 52 56 42 79 7,7 3,39 9,6 69,2 2302 22,2 41,3 24,2 18 8 27Chicago, IL 1159,89 33 58 26 76 8,6 3,2 10,9 83,4 6122 16,3 44,9 10,7 88 63 278Richmond, VA 1160,5 44 53 39 78 8,2 3,32 9,8 79,9 3768 28,6 49,5 17,5 12 9 48Birmingham, AL 1165,38 53 54 45 80 7,7 3,45 10,2 66,8 3235 38,5 43,1 25,5 30 32 72Baltimore, MD 1206,29 43 55 35 77 7,6 3,44 9,6 84,6 6441 24,4 43,7 14,3 43 38 206New Orleans, LA 1248,06 54 62 54 81 7,4 3,36 9,7 72,8 3172 31,4 45,5 24,2 20 17 1       MathStatistics and ProbabilitymatlabBUAN 6356Share Question