Cardiovascular disease is the leading cause of death of people in the United States. Every year about 697,000 people die of heart disease (Centers for Disease Control and Prevention, 2022). Cardiovascular disease is comprised of numerous conditions such as heart failure, coronary heart disease, or any other condition affecting the heart and blood vessels. Cerebrovascular disease, or strokes, occur when the blood supply to the brain is interrupted. Both of these diseases disproportionately affect low- and middle-income populations (Kelli, et.al 2018). Some of the measures associated with both conditions are income level, education, employment status, and socioeconomic factors. The relationship between diet and exercise and cardiovascular and cerebrovascular disease is crucial in maintaining a healthy cardiovascular system and reducing the risk of these conditions.

For my final assignment, I used the dataset “Community Health Obesity and Diabetes Related Indicators: 2008-2012”( Health.data.ny.gov., 2021 ). It is comprised of 63 New York counties and their region names along with numerous health indicators such as diabetes and obesity hospitalizations for both adults and children, cirrhosis mortality rates, diet and exercise habits, and others. Given the prevalent mortality rates in the U.S, I was interested in analyzing the difference in means of cardiovascular and cerebrovascular mortality rates per 100,000 people across the nine regions of New York. I was also interested in verifying whether there was a liner relationship between cardiovascular and cerebrovascular disease mortality rates and diet (age-adjusted percentage of adults eating 5 or more fruits or vegetables per day at a 95% CI), lack of exercise (age-adjusted percentage of adults who did not participate in leisure time physical activity in last 30 days at a 95% CI.), and region.

For my first analysis, I conducted factorial ANOVA using cardiovascular and cerebrovascular mortality rates as my dependent variable and NY’s regions as my independent variable. The null hypothesis was that the means of means of cardiovascular and cerebrovascular mortality rates were the same. The alternate hypothesis was that the means of cardiovascular and cerebrovascular mortality rates were not the same. I also included interaction hypothesis. For my interaction null hypothesis, there were no interactions among cardiovascular and cerebrovascular mortality rates against regions. My interaction alternate hypothesis was there were interactions among cardiovascular and cerebrovascular mortality rates against regions. I used f-test to make the statistical inference at a=0.05. If the p-value was less than alpha, we rejected the null-hypothesis and infer that there were differences among the means. If p-value was less than alpha for interactions, we concluded that there were significant interactions across the factors

ny_fit = manova(cbind(Cardiovascular.Mortality, Cerebrovascular.Mortality)~ `Region Name`)
summary(ny_fit)
##               Df  Pillai approx F num Df den Df    Pr(>F)    
## `Region Name`  8 0.91817   5.7289     16    108 8.522e-09 ***
## Residuals     54                                             
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
summary.aov(ny_fit)
##  Response Cardiovascular.Mortality :
##               Df Sum Sq Mean Sq F value  Pr(>F)  
## `Region Name`  8  74168  9271.0  2.7946 0.01153 *
## Residuals     54 179147  3317.5                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##  Response Cerebrovascular.Mortality :
##               Df Sum Sq Mean Sq F value    Pr(>F)    
## `Region Name`  8 4689.8  586.22  12.843 3.867e-10 ***
## Residuals     54 2464.9   45.65                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Based on the model above, we can see that the p-value was less than 0.05 therefore, we can reject the null hypothesis. There were significant differences among the means for cardiovascular and cerebrovascular mortality rates. There were also interactions among both factors on regions.

I also conducted a post hoc Tukey Test to verify which two pairs had significant differences. For cardiovascular mortality rates, we can see that Western New York and Hudson Valley had a p-value of 0.0303363, making them the most significantly different. For cerebrovascular mortality rates, there were several regions that had significant differences. The most significantly different pairs were New York City and Finger Lakes, Northeastern New York and New York City, and Western New York and New York City all with a p-value of 0.0000001. Below is screenshot of the post hoc Tukey Test results:

ny_fit1Tukey = aov(Cardiovascular.Mortality ~ factor(`Region Name`), data = ny_data)
summary(ny_fit1Tukey)
##                       Df Sum Sq Mean Sq F value Pr(>F)  
## factor(`Region Name`)  8  74168    9271   2.795 0.0115 *
## Residuals             54 179147    3318                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(ny_fit1Tukey)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Cardiovascular.Mortality ~ factor(`Region Name`), data = ny_data)
## 
## $`factor(`Region Name`)`
##                                              diff         lwr       upr
## Finger Lakes-Central New York            3.836364  -79.802605  87.47533
## Hudson Valley-Central New York         -32.135065 -122.105985  57.83585
## Nassau-Suffolk-Central New York         18.336364 -124.708282 161.38101
## New York-Penn-Central New York          71.103030  -50.101351 192.30741
## New York City-Central New York         -26.783636 -127.150399  73.58313
## New York State-Central New York         -8.263636 -202.623036 186.09576
## Northeastern New York-Central New York  43.012834  -28.993298 115.01897
## Western New York-Central New York       69.811364  -16.654908 156.27764
## Hudson Valley-Finger Lakes             -35.971429 -129.749433  57.80658
## Nassau-Suffolk-Finger Lakes             14.500000 -130.969304 159.96930
## New York-Penn-Finger Lakes              67.266667  -56.789972 191.32331
## New York City-Finger Lakes             -30.620000 -134.413231  73.17323
## New York State-Finger Lakes            -12.100000 -208.250769 184.05077
## Northeastern New York-Finger Lakes      39.176471  -37.533573 115.88651
## Western New York-Finger Lakes           65.975000  -24.446037 156.39604
## Nassau-Suffolk-Hudson Valley            50.471429  -98.728463 199.67132
## New York-Penn-Hudson Valley            103.238095  -25.172726 231.64892
## New York City-Hudson Valley              5.351429 -103.608766 114.31162
## New York State-Hudson Valley            23.871429 -175.061760 222.80462
## Northeastern New York-Hudson Valley     75.147899   -8.420755 158.71655
## Western New York-Hudson Valley         101.946429    5.638313 198.25454
## New York-Penn-Nassau-Suffolk            52.766667 -117.104882 222.63822
## New York City-Nassau-Suffolk           -45.120000 -200.809846 110.56985
## New York State-Nassau-Suffolk          -26.600000 -254.506598 201.30660
## Northeastern New York-Nassau-Suffolk    24.676471 -114.430410 163.78335
## Western New York-Nassau-Suffolk         51.475000  -95.638077 198.58808
## New York City-New York-Penn            -97.886667 -233.783906  38.01057
## New York State-New York-Penn           -79.366667 -294.239068 135.50573
## Northeastern New York-New York-Penn    -28.090196 -144.621117  88.44073
## Western New York-New York-Penn          -1.291667 -127.271779 124.68845
## New York State-New York City            18.520000 -185.325859 222.36586
## Northeastern New York-New York City     69.796471  -24.873697 164.46664
## Western New York-New York City          96.595000   -9.489748 202.67975
## Northeastern New York-New York State    51.276471 -140.203372 242.75631
## Western New York-New York State         78.075000 -119.297904 275.44790
## Western New York-Northeastern New York  26.798529  -52.984738 106.58180
##                                            p adj
## Finger Lakes-Central New York          1.0000000
## Hudson Valley-Central New York         0.9625381
## Nassau-Suffolk-Central New York        0.9999719
## New York-Penn-Central New York         0.6197978
## New York City-Central New York         0.9940387
## New York State-Central New York        1.0000000
## Northeastern New York-Central New York 0.5968282
## Western New York-Central New York      0.2072971
## Hudson Valley-Finger Lakes             0.9437791
## Nassau-Suffolk-Finger Lakes            0.9999960
## New York-Penn-Finger Lakes             0.7122793
## New York City-Finger Lakes             0.9884582
## New York State-Finger Lakes            0.9999999
## Northeastern New York-Finger Lakes     0.7729623
## Western New York-Finger Lakes          0.3279830
## Nassau-Suffolk-Hudson Valley           0.9728569
## New York-Penn-Hudson Valley            0.2118419
## New York City-Hudson Valley            1.0000000
## New York State-Hudson Valley           0.9999831
## Northeastern New York-Hudson Valley    0.1102021
## Western New York-Hudson Valley         0.0303363
## New York-Penn-Nassau-Suffolk           0.9839598
## New York City-Nassau-Suffolk           0.9897149
## New York State-Nassau-Suffolk          0.9999863
## Northeastern New York-Nassau-Suffolk   0.9996720
## Western New York-Nassau-Suffolk        0.9667971
## New York City-New York-Penn            0.3448155
## New York State-New York-Penn           0.9545372
## Northeastern New York-New York-Penn    0.9970230
## Western New York-New York-Penn         1.0000000
## New York State-New York City           0.9999981
## Northeastern New York-New York City    0.3146074
## Western New York-New York City         0.1013307
## Northeastern New York-New York State   0.9938975
## Western New York-New York State        0.9334433
## Western New York-Northeastern New York 0.9739940
ny_fit2Tukey = aov(Cerebrovascular.Mortality ~ factor(`Region Name`), data = ny_data)
summary(ny_fit2Tukey)
##                       Df Sum Sq Mean Sq F value   Pr(>F)    
## factor(`Region Name`)  8   4690   586.2   12.84 3.87e-10 ***
## Residuals             54   2465    45.6                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(ny_fit2Tukey)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Cerebrovascular.Mortality ~ factor(`Region Name`), data = ny_data)
## 
## $`factor(`Region Name`)`
##                                               diff           lwr          upr
## Finger Lakes-Central New York            0.6424242  -9.168298934  10.45314742
## Hudson Valley-Central New York         -15.9194805 -26.472931836  -5.36602920
## Nassau-Suffolk-Central New York        -16.3409091 -33.119827293   0.43800911
## New York-Penn-Central New York           2.9090909 -11.307997661  17.12617948
## New York City-Central New York         -26.7709091 -38.543776902 -14.99804128
## New York State-Central New York        -15.0909091 -37.888969576   7.70715139
## Northeastern New York-Central New York  -2.6026738 -11.048882986   5.84353539
## Western New York-Central New York        0.9090909  -9.233270583  11.05145240
## Hudson Valley-Finger Lakes             -16.5619048 -27.561921290  -5.56188823
## Nassau-Suffolk-Finger Lakes            -16.9833333 -34.046660235   0.07999357
## New York-Penn-Finger Lakes               2.2666667 -12.284987409  16.81832074
## New York City-Finger Lakes             -27.4133333 -39.588120618 -15.23854605
## New York State-Finger Lakes            -15.7333333 -38.741518634   7.27485197
## Northeastern New York-Finger Lakes      -3.2450980 -12.243068844   5.75287277
## Western New York-Finger Lakes            0.2666667 -10.339582696  10.87291603
## Nassau-Suffolk-Hudson Valley            -0.4214286 -17.922347702  17.07949056
## New York-Penn-Hudson Valley             18.8285714   3.766178465  33.89096439
## New York City-Hudson Valley            -10.8514286 -23.632292818   1.92943567
## New York State-Hudson Valley             0.8285714 -22.505987412  24.16313027
## Northeastern New York-Hudson Valley     13.3168067   3.514331319  23.11928213
## Western New York-Hudson Valley          16.8285714   5.531776706  28.12536615
## New York-Penn-Nassau-Suffolk            19.2500000  -0.675672965  39.17567297
## New York City-Nassau-Suffolk           -10.4300000 -28.692180927   7.83218093
## New York State-Nassau-Suffolk            1.2500000 -25.483095549  27.98309555
## Northeastern New York-Nassau-Suffolk    13.7382353  -2.578789109  30.05525970
## Western New York-Nassau-Suffolk         17.2500000  -0.006138975  34.50613898
## New York City-New York-Penn            -29.6800000 -45.620538372 -13.73946163
## New York State-New York-Penn           -18.0000000 -43.204204193   7.20420419
## Northeastern New York-New York-Penn     -5.5117647 -19.180663592   8.15713418
## Western New York-New York-Penn          -2.0000000 -16.777274570  12.77727457
## New York State-New York City            11.6800000 -12.230807558  35.59080756
## Northeastern New York-New York City     24.1682353  13.063569344  35.27290124
## Western New York-New York City          27.6800000  15.236421222  40.12357878
## Northeastern New York-New York State    12.4882353  -9.972057475  34.94852806
## Western New York-New York State         16.0000000  -7.151539867  39.15153987
## Western New York-Northeastern New York   3.5117647  -5.846690614  12.87022003
##                                            p adj
## Finger Lakes-Central New York          0.9999999
## Hudson Valley-Central New York         0.0003238
## Nassau-Suffolk-Central New York        0.0619076
## New York-Penn-Central New York         0.9990676
## New York City-Central New York         0.0000000
## New York State-Central New York        0.4591752
## Northeastern New York-Central New York 0.9847517
## Western New York-Central New York      0.9999983
## Hudson Valley-Finger Lakes             0.0003341
## Nassau-Suffolk-Finger Lakes            0.0519779
## New York-Penn-Finger Lakes             0.9998759
## New York City-Finger Lakes             0.0000001
## New York State-Finger Lakes            0.4146541
## Northeastern New York-Finger Lakes     0.9603691
## Western New York-Finger Lakes          1.0000000
## Nassau-Suffolk-Hudson Valley           1.0000000
## New York-Penn-Hudson Valley            0.0049956
## New York City-Hudson Valley            0.1574265
## New York State-Hudson Valley           1.0000000
## Northeastern New York-Hudson Valley    0.0016395
## Western New York-Hudson Valley         0.0003985
## New York-Penn-Nassau-Suffolk           0.0659141
## New York City-Nassau-Suffolk           0.6527334
## New York State-Nassau-Suffolk          1.0000000
## Northeastern New York-Nassau-Suffolk   0.1651907
## Western New York-Nassau-Suffolk        0.0501477
## New York City-New York-Penn            0.0000055
## New York State-New York-Penn           0.3561110
## Northeastern New York-New York-Penn    0.9262125
## Western New York-New York-Penn         0.9999573
## New York State-New York City           0.8121237
## Northeastern New York-New York City    0.0000001
## Western New York-New York City         0.0000001
## Northeastern New York-New York State   0.6842352
## Western New York-New York State        0.4002308
## Western New York-Northeastern New York 0.9502758

I also created a box plot of the data using ggplot (Bedre, 2021) to help visualize the data and see the differences between the regions for cardiovascular and cerebrovascular mortality rates. With the graph below, we can easily identify the disparities across the regions.

library(gridExtra)
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.2.3
p1 = ggplot(ny_data, aes(x = `Region Name`, y = Cardiovascular.Mortality, fill = `Region Name`)) + geom_boxplot(outlier.shape = NA) + geom_jitter(width = 0.2) + theme(legend.position="top") + theme(axis.text.x =  element_text(size = 5))
p2 = ggplot(ny_data, aes(x = `Region Name`, y = Cerebrovascular.Mortality, fill = `Region Name`)) + geom_boxplot(outlier.shape = NA) + geom_jitter(width = 0.2) + theme(legend.position="top")+ theme(axis.text.x = element_text(size = 5))
grid.arrange(p1,p2, ncol=2)

To verify if there was a liner relationship between cardiovascular and cerebrovascular disease mortality rates and diet (age-adjusted percentage of adults eating 5 or more fruits or vegetables per day at a 95% CI), lack of exercise (age-adjusted percentage of adults who did not participate in leisure time physical activity in last 30 days at a 95% CI.), and regions, I conducted a multilinear regression. My null hypothesis was that the percentages of adults eating 5 or more fruits and vegetables p/day, the percentages of adults who did not participate in leisure time physical activity in the last 30 days, and Regions of New York were not predictors of cardiovascular mortality rates and cerebrovascular rates. My alternate hypothesis was that the percentages of adults eating 5 or more fruits and vegetables p/day, and/or the percentages of adults who did not participate in leisure time physical activity in the last 30 days, and/or Regions of New York were/are predictors of cardiovascular mortality rates and cerebrovascular rates. I used the F-test statistical inference at 0.01. If the p-value was less than 0.01, we rejected the null hypothesis. Below is a screenshot of the R-code and model:

cardiocerebrolm= lm(cbind(Cardiovascular.Mortality, Cerebrovascular.Mortality) ~ `Adults eating 5 or more fruits or vegetables per day`+
                      `Adults who did not participate in leisure time physical activity in last 30 days`
                    + factor(`Region Name`))
summary(cardiocerebrolm)
## Response Cardiovascular.Mortality :
## 
## Call:
## lm(formula = Cardiovascular.Mortality ~ `Adults eating 5 or more fruits or vegetables per day` + 
##     `Adults who did not participate in leisure time physical activity in last 30 days` + 
##     factor(`Region Name`))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -130.94  -39.78   -3.17   30.22  121.57 
## 
## Coefficients:
##                                                                                    Estimate
## (Intercept)                                                                         507.923
## `Adults eating 5 or more fruits or vegetables per day`                               -3.236
## `Adults who did not participate in leisure time physical activity in last 30 days`   -1.691
## factor(`Region Name`)Finger Lakes                                                     8.463
## factor(`Region Name`)Hudson Valley                                                  -26.738
## factor(`Region Name`)Nassau-Suffolk                                                  20.025
## factor(`Region Name`)New York-Penn                                                   67.981
## factor(`Region Name`)New York City                                                  -92.394
## factor(`Region Name`)New York State                                                 -10.033
## factor(`Region Name`)Northeastern New York                                           43.084
## factor(`Region Name`)Western New York                                                57.412
##                                                                                    Std. Error
## (Intercept)                                                                           176.362
## `Adults eating 5 or more fruits or vegetables per day`                                  2.561
## `Adults who did not participate in leisure time physical activity in last 30 days`      2.337
## factor(`Region Name`)Finger Lakes                                                      25.855
## factor(`Region Name`)Hudson Valley                                                     28.317
## factor(`Region Name`)Nassau-Suffolk                                                    43.945
## factor(`Region Name`)New York-Penn                                                     38.159
## factor(`Region Name`)New York City                                                     52.843
## factor(`Region Name`)New York State                                                    59.803
## factor(`Region Name`)Northeastern New York                                             22.999
## factor(`Region Name`)Western New York                                                  27.596
##                                                                                    t value
## (Intercept)                                                                          2.880
## `Adults eating 5 or more fruits or vegetables per day`                              -1.264
## `Adults who did not participate in leisure time physical activity in last 30 days`  -0.723
## factor(`Region Name`)Finger Lakes                                                    0.327
## factor(`Region Name`)Hudson Valley                                                  -0.944
## factor(`Region Name`)Nassau-Suffolk                                                  0.456
## factor(`Region Name`)New York-Penn                                                   1.782
## factor(`Region Name`)New York City                                                  -1.748
## factor(`Region Name`)New York State                                                 -0.168
## factor(`Region Name`)Northeastern New York                                           1.873
## factor(`Region Name`)Western New York                                                2.080
##                                                                                    Pr(>|t|)
## (Intercept)                                                                         0.00576
## `Adults eating 5 or more fruits or vegetables per day`                              0.21203
## `Adults who did not participate in leisure time physical activity in last 30 days`  0.47276
## factor(`Region Name`)Finger Lakes                                                   0.74472
## factor(`Region Name`)Hudson Valley                                                  0.34943
## factor(`Region Name`)Nassau-Suffolk                                                 0.65051
## factor(`Region Name`)New York-Penn                                                  0.08067
## factor(`Region Name`)New York City                                                  0.08629
## factor(`Region Name`)New York State                                                 0.86741
## factor(`Region Name`)Northeastern New York                                          0.06665
## factor(`Region Name`)Western New York                                               0.04243
##                                                                                      
## (Intercept)                                                                        **
## `Adults eating 5 or more fruits or vegetables per day`                               
## `Adults who did not participate in leisure time physical activity in last 30 days`   
## factor(`Region Name`)Finger Lakes                                                    
## factor(`Region Name`)Hudson Valley                                                   
## factor(`Region Name`)Nassau-Suffolk                                                  
## factor(`Region Name`)New York-Penn                                                 . 
## factor(`Region Name`)New York City                                                 . 
## factor(`Region Name`)New York State                                                  
## factor(`Region Name`)Northeastern New York                                         . 
## factor(`Region Name`)Western New York                                              * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 57.15 on 52 degrees of freedom
## Multiple R-squared:  0.3296, Adjusted R-squared:  0.2006 
## F-statistic: 2.556 on 10 and 52 DF,  p-value: 0.01361
## 
## 
## Response Cerebrovascular.Mortality :
## 
## Call:
## lm(formula = Cerebrovascular.Mortality ~ `Adults eating 5 or more fruits or vegetables per day` + 
##     `Adults who did not participate in leisure time physical activity in last 30 days` + 
##     factor(`Region Name`))
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -15.416  -3.218   0.000   3.370  13.266 
## 
## Coefficients:
##                                                                                     Estimate
## (Intercept)                                                                         35.97832
## `Adults eating 5 or more fruits or vegetables per day`                              -0.42712
## `Adults who did not participate in leisure time physical activity in last 30 days`   0.27758
## factor(`Region Name`)Finger Lakes                                                    1.02704
## factor(`Region Name`)Hudson Valley                                                 -14.79418
## factor(`Region Name`)Nassau-Suffolk                                                -16.35244
## factor(`Region Name`)New York-Penn                                                   1.40310
## factor(`Region Name`)New York City                                                 -32.72582
## factor(`Region Name`)New York State                                                -14.58252
## factor(`Region Name`)Northeastern New York                                          -3.65383
## factor(`Region Name`)Western New York                                                0.09582
##                                                                                    Std. Error
## (Intercept)                                                                          20.77037
## `Adults eating 5 or more fruits or vegetables per day`                                0.30162
## `Adults who did not participate in leisure time physical activity in last 30 days`    0.27528
## factor(`Region Name`)Finger Lakes                                                     3.04493
## factor(`Region Name`)Hudson Valley                                                    3.33496
## factor(`Region Name`)Nassau-Suffolk                                                   5.17547
## factor(`Region Name`)New York-Penn                                                    4.49406
## factor(`Region Name`)New York City                                                    6.22340
## factor(`Region Name`)New York State                                                   7.04304
## factor(`Region Name`)Northeastern New York                                            2.70856
## factor(`Region Name`)Western New York                                                 3.25006
##                                                                                    t value
## (Intercept)                                                                          1.732
## `Adults eating 5 or more fruits or vegetables per day`                              -1.416
## `Adults who did not participate in leisure time physical activity in last 30 days`   1.008
## factor(`Region Name`)Finger Lakes                                                    0.337
## factor(`Region Name`)Hudson Valley                                                  -4.436
## factor(`Region Name`)Nassau-Suffolk                                                 -3.160
## factor(`Region Name`)New York-Penn                                                   0.312
## factor(`Region Name`)New York City                                                  -5.259
## factor(`Region Name`)New York State                                                 -2.070
## factor(`Region Name`)Northeastern New York                                          -1.349
## factor(`Region Name`)Western New York                                                0.029
##                                                                                    Pr(>|t|)
## (Intercept)                                                                         0.08917
## `Adults eating 5 or more fruits or vegetables per day`                              0.16272
## `Adults who did not participate in leisure time physical activity in last 30 days`  0.31797
## factor(`Region Name`)Finger Lakes                                                   0.73725
## factor(`Region Name`)Hudson Valley                                                 4.78e-05
## factor(`Region Name`)Nassau-Suffolk                                                 0.00263
## factor(`Region Name`)New York-Penn                                                  0.75613
## factor(`Region Name`)New York City                                                 2.77e-06
## factor(`Region Name`)New York State                                                 0.04339
## factor(`Region Name`)Northeastern New York                                          0.18318
## factor(`Region Name`)Western New York                                               0.97659
##                                                                                       
## (Intercept)                                                                        .  
## `Adults eating 5 or more fruits or vegetables per day`                                
## `Adults who did not participate in leisure time physical activity in last 30 days`    
## factor(`Region Name`)Finger Lakes                                                     
## factor(`Region Name`)Hudson Valley                                                 ***
## factor(`Region Name`)Nassau-Suffolk                                                ** 
## factor(`Region Name`)New York-Penn                                                    
## factor(`Region Name`)New York City                                                 ***
## factor(`Region Name`)New York State                                                *  
## factor(`Region Name`)Northeastern New York                                            
## factor(`Region Name`)Western New York                                                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.73 on 52 degrees of freedom
## Multiple R-squared:  0.6708, Adjusted R-squared:  0.6074 
## F-statistic: 10.59 on 10 and 52 DF,  p-value: 1.704e-09

Based on the models above, we cannot reject the null hypothesis for cardiovascular mortality rates. The p-value was greater than 0.01. There was no significant evidence that the percentages of adults eating 5 or more fruits and vegetables per day, percentages of adults who did not participate in leisure time physical activity in last 30 days, and the regions of New York when taken together were predictive of cardiovascular mortality rates.

For cerebrovascular mortality rates, the p-value was less than 0.01. We can reject the null hypothesis. There is significant evidence that the percentages of adults eating 5 or more fruits and vegetables per day, percentages of adults who did not participate in leisure time physical activity in last 30 days, and the regions of New York when taken together were predictive of cerebrovascular mortality rates. More specifically, the regions of Hudson Valley, Nassau-Folk, and New York City were significant predictors of cerebrovascular mortality rates.

While conducting my analyses, I did encounter some limitations. For the multilinear regression, I received a masking error which I was unable to solve. It analyzed 8 out of the 9 regions. I also wanted to get a clearer criterion of cardiovascular disease. Cardiovascular disease can be numerous conditions such as congenital or hereditary conditions. I believe this could’ve improved my analyses by being more specific on the exact mortality cause.

References
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Centers for Disease Control and Prevention. (2022, October 14). Stroke facts. Centers for Disease Control and Prevention. Retrieved April 29, 2023, from https://www.cdc.gov/stroke/facts.htm#:~:text=Stroke%20statistics,-In%202020%2C%201&text=Every%20year%2C%20more%20than%20795%2C000,are%20first%20or%20new%20strokes.&text=About%20185%2C000%20strokes%E2%80%94nearly%201,have%20had%20a%20previous%20stroke.&text=About%2087%25%20of%20all%20strokes,to%20the%20brain%20is%20blocked.

Danielle Navarro (bookdown translation: Emily Kothe). (2019, January 11). Learning statistics with R: A tutorial for psychology students and other beginners. (version 0.6.1). Chapter 16 Factorial ANOVA. Retrieved April 29, 2023, from https://learningstatisticswithr.com/book/anova2.html#factorialanovasimple

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Zach. (2022, February 23). How to plot multiple linear regression results in R. Statology. Retrieved April 29, 2023, from https://www.statology.org/plot-multiple-linear-regression-in-r/