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Compute Regression Analysis for following relationship: The relationship between death rate X1 (USD) vs. population density...

Compute Regression Analysis for following relationship: The relationship between death rate X1 (USD) vs. population density X5. Population as a Predictor, X, then death rate as a Response variable, Y. Get Regression Output, and Scatter plot between these variables and compute Coefficient of Determination, R2, and Interpret your findings.

X1  X2  X3   X4     X5   The data (X1, X2, X3, X4, X5) are by city.      
8   78   284   9.1   109   X1 = death rate per 1000 residents      
9.3   68   433   8.7   144 X2 = doctor availability per 100,000 residents  
7.5   70   739   7.2   113  X3 = hospital availability per 100,000 residents  
8.9   96   1792   8.9   97  X4 = annual per capita income in thousands of dollars  
10.2   74   477   8.3   206  X5 = population density people per square mile  
8.3   111   362   10.9   124   
8.8   77   671   10   152                              
8.8   168   636   9.1   162                              
10.7   82   329   8.7   150                              
11.7   89   634   7.6   134                              
8.5   149   631   10.8   292                              
8.3   60   257   9.5   108                              
8.2   96   284   8.8   111                              
7.9   83   603   9.5   182                              
10.3   130   686   8.7   129                              
7.4   145   345   11.2   158                              
9.6   112   1357   9.7   186                              
9.3   131   544   9.6   177                              
10.6   80   205   9.1   127                              
9.7   130   1264   9.2   179                              
11.6   140   688   8.3   80                              
8.1   154   354   8.4   103                              
9.8   118   1632   9.4   101                              
7.4   94   348   9.8   117                              
9.4   119   370   10.4   88                              
11.2   153   648   9.9   78                              
9.1   116   366   9.2   102                              
10.5   97   540   10.3   95                              
11.9   176   680   8.9   80                              
8.4   75   345   9.6   92                              
5   134   525   10.3   126                              
9.8   161   870   10.4   108                              
9.8   111   669   9.7   77                              
10.8   114   452   9.6   60                              
10.1   142   430   10.7   71                              
10.9   238   822   10.3   86                              
9.2   78   190   10.7   93                              
8.3   196   867   9.6   106                              
7.3   125   969   10.5   162                              
9.4   82   499   7.7   95                              
9.4   125   925   10.2   91                              
9.8   129   353   9.9   52                              
3.6   84   288   8.4   110                              
8.4   183   718   10.4   69                              
10.8   119   540   9.2   57                              
10.1   180   668   13   106                              
9   82   347   8.8   40                              
10   71   345   9.2   50                              
11.3   118   463   7.8   35                              
11.3   121   728   8.2   86                              
12.8   68   383   7.4   57                              
10   112   316   10.4   57                              
6.7   109   388   8.9   94                              

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Answer #1

13.6 9 9.6 7.6 5.6 3.6 30 70 110 150 90 230 270 310 x-Independent -001X + 10.39) _ Regression Line (y

X - Mx Y - My (X - Mx)2 (X - Mx)(Y - My)
-1.6415 -1.3057 2.6946 2.1433
33.3585 -0.0057 1112.7889 -0.1888
2.3585 -1.8057 5.5625 -4.2586
-13.6415 -0.4057 186.0908 5.5338
95.3585 0.8943 9093.2417 85.2829
13.3585 -1.0057 178.4493 -13.4341
41.3585 -0.5057 1710.5247 -20.9133
51.3585 -0.5057 2637.6946 -25.97
39.3585 1.3943 1549.0908 54.8791
23.3585 2.3943 545.6191 55.9282
181.3585 -0.8057 32890.9021 -146.1133
-2.6415 -1.0057 6.9776 2.6565
0.3585 -1.1057 0.1285 -0.3964
71.3585 -1.4057 5092.0342 -100.3058
18.3585 0.9943 337.0342 18.2546
47.3585 -1.9057 2242.8266 -90.2492
75.3585 0.2943 5678.9021 22.181
66.3585 -0.0057 4403.4493 -0.3756
16.3585 1.2943 267.6002 21.1734
68.3585 0.3943 4672.8832 26.9565
-30.6415 2.2943 938.9021 -70.302
-7.6415 -1.2057 58.3927 9.2131
-9.6415 0.4943 92.9587 -4.7662
6.3585 -1.9057 40.4304 -12.1171
-22.6415 0.0943 512.6379 -2.136
-32.6415 1.8943 1065.4681 -61.8341
-8.6415 -0.2057 74.6757 1.7772
-15.6415 1.1943 244.6568 -18.6813
-30.6415 2.5943 938.9021 -79.4945
-18.6415 -0.9057 347.5059 16.8829
15.3585 -4.3057 235.8832 -66.1284
-2.6415 0.4943 6.9776 -1.3058
-33.6415 0.4943 1131.7512 -16.6303
-50.6415 1.4943 2564.5625 -75.6756
-39.6415 0.7943 1571.4493 -31.4888
-24.6415 1.5943 607.204 -39.2869
-17.6415 -0.1057 311.2229 1.864
-4.6415 -1.0057 21.5436 4.6678
51.3585 -2.0057 2637.6946 -103.0077
-15.6415 0.0943 244.6568 -1.4756
-19.6415 0.0943 385.7889 -1.853
-58.6415 0.4943 3438.8266 -28.9888
-0.6415 -5.7057 0.4115 3.6602
-41.6415 -0.9057 1734.0153 37.7131
-53.6415 1.4943 2877.4115 -80.1586
-4.6415 0.7943 21.5436 -3.6869
-70.6415 -0.3057 4990.2229 21.5923
-60.6415 0.6943 3677.3927 -42.1058
-75.6415 1.9943 5721.6379 -150.8549
-24.6415 1.9943 607.204 -49.1435
-53.6415 3.4943 2877.4115 -187.4417
-53.6415 0.6943 2877.4115 -37.2454
-16.6415 -2.6057 276.9398 43.3621
SS: 115748.1887 SP: -1132.2925

Sum of X = 5864
Sum of Y = 493.2
Mean X = 110.6415
Mean Y = 9.3057
Sum of squares (SSX) = 115748.1887
Sum of products (SP) = -1132.2925

Regression Equation = ŷ = bX + a

b = SP/SSX = -1132.29/115748.19 = -0.00978

a = MY - bMX = 9.31 - (-0.01*110.64) = 10.388

ŷ = -0.00978X + 10.388

X Values
∑ = 5864
Mean = 110.642
∑(X - Mx)2 = SSx = 115748.189

Y Values
∑ = 493.2
Mean = 9.306
∑(Y - My)2 = SSy = 143.728

X and Y Combined
N = 53
∑(X - Mx)(Y - My) = -1132.292

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -1132.292 / √((115748.189)(143.728))

r = -0.2776

The value of R is -0.2776

The value of R2, the coefficient of determination, is 0.0771

Output from excel

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.277606968
R Square 0.077065629
Adjusted R Square 0.058968877
Standard Error 1.612766408
Observations 53
ANOVA
df SS MS F Significance F
Regression 1 11.07651198 11.07651198 4.25853365 0.044160289
Residual 51 132.6517899 2.601015488
Total 52 143.7283019
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 10.38799737 0.569350071 18.24536063 5.2651E-24 9.24497943 11.5310153 9.24497943 11.5310153
x -0.009782377 0.004740393 -2.063621489 0.044160289 -0.019299114 -0.000265641 -0.019299114 -0.000265641

Although technically a negative correlation, the relationship between your variables is only weak (nb. the nearer the value is to zero, the weaker the relationship)

If population density people per square mile increases then death rate per 1000 residents decreases( decrease rate = 1%)

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