In the assessment of population health and overall well-being in a given country, there are several factors to consider; such as, the prevalence of diseases, life expectancy, and average death rate with regards to region, age, year, and race. The information obtained from these assessment tests will aid with the determination of whether or not the country being evaluated has an effective healthcare system and the government has put in place the proper regulations and incentives to boost food availability, nutrition, and disease control. For instance health data collected from all States across the United States of America over the last five decades will aid in understanding whether or not the quality of life for Americans has improved in the last ten years. In the same way, race centric data can be used to assess inequalities of healthcare services with regard to race. For instance, more white people could be accessing quality healthcare services compared to black individuals with the same income per capita. Moreover, examination of data with regard to regions and states helps with the recognition of correlation between different variables in the diverse categories. According to most medical professionals, women are more likely to solicit healthcare service compared to men suffering from the same physical and mental ailment. This situation has led physicians to believe that men have a lower life expectancy compared to women; and in addition, they are more at risk of succumbing to death as a result of failure to secure medical treatment at the proper time.
In the United States of America, organizations like the Centers for Disease Control and Prevention (CDC) collect, compile, analysis, and present data related to difference medical conditions. These data is then made accessible to all individuals, groups, and agencies for the purposes of their own independent research studies. The data is normally archived in a chronological manner to ensure that trend analysis can be easily performed to identify whether or not advancements in healthcare delivery have positively impacted the medical profession. As such, the study of data relating to diseases is aimed at providing a realistic scope over the current and past healthcare trends. Once this information is obtained it can be used by the proper stakeholders to ensure that people of all races and gender are provided with quality healthcare across all States in future. The formulation process for an effective healthcare reform plan normally takes into account the opinions and suggestions of medical professionals, government agencies, NGO representatives, and given members of society. In conclusion, the data will be analyzed with the primary objective of assessing the impact of gender, and demographic on the life expectancy and death rate in the United States of America.
There are two sets of possess both quantitative and qualitative data that need to be analyzed. One data set is centered on the evaluation of different disease causation, and deaths across all 52 States over the past 16 years. The data is classified under six categories: year, 113 cause name, cause name, state, deaths, and age-adjusted death rate. There are over 15 disease causes that are presented with regard to the 52 states. The figures for deaths and age adjusted death rate associated with each disease are provided in a chronological manner starting from the year 1999 to 2015. Lately, the data is comprehensive and large enough for proper inferences to be made with regard to the overall medical system observed in individual States across the United States of America. As such, the results produced after analysis can be indicated as the accurate representation of the healthcare and morbidity situation in America. The other data set evaluates life expectancy and age-adjusted death rate data will regard to gender and race. The data is classified under five distinct categories: year, race, sex, average life expectancy, and age-adjusted death rate. Similarly, this data set is also arranged in a chronological order with data ranging from 1900 to 2015; roughly 115 years. This data set is therefore significantly more comprehensive and inclusive compared to the latter, simply because it employs a wide-time frame of data collection. Nevertheless, this does also present problems because of significant differences in lifestyle and healthcare services present between 1900 and 2015. For instance, diseases like HIV/AIDS were not present for the better part of the 1900s; this disease has become a critical cause of 400,000 deaths annually in the United States of America. This information can be ignored or be cancelled out by the fact that deaths attributed to smallpox and polio have almost vanished over the past three decades.
The two data sets can be easily analyzed to check for outliners, correlation, skewness, and other crucial information. As such, a quantitative research method will be employed that will allow for establishment of relationships between different variables in the data sets. A descriptive approach is used in the process because the data was measured and collected once; unlike in an experimental approach where the data is collect before and after treatment. The mainly reason for using a quantitative research method is because: the sample sizes are large; the data was gathered using structured collection media; there is need to use a statistical tool/software; there are defined research objectives; and lastly the data is in numerical form or can be assigned numerical equivalents. As such, the analysis will take into account a lot of diagrammatical and graphical representation to aid in the explanation of various analysis results. Assumptions will be made where necessary to ensure that the information presented is governed within given parameters. Lastly, the results of the analysis will be employed in the development of recommendation; independent of the researcher’s own research expectations.
Missing data will be treated in different ways depending on the statistical analysis being run. For instance, in a correlation assessment all variables being evaluated need to have the same frequency; therefore, if two variables have 155 and the three has 154, the row with the missing data for all three will be disregarded. Hence, all three will have 154 items to be employed in the correlation analysis. On the other hand, if the data is being evaluated for descriptive statistics e.g. mean, median, variances, and skewness; the missing values will be ignored entirely but will not affect the assessment of the next variable. For instance, if we are to find the mean for each of two variables where one has 155 rows of data but 7 of those rows are empty, and another has 155 data items in every row. Then, the assessment of mean will be performed on only 148 items for the first variable; but, on 155 items for the second. Lastly, in a regression analysis the empty data cells can be treated as being occupied by zeros or be disregarded. For this assessment the cells will be ignored; As such, the entire row will be ignored for both the dependent and independent variables regardless of which has missing cell data.
The Data will be assessed with the aid of Weka assessment platform and Microsoft Excel to provide a detailed and accurate data evaluation. Important analysis outputs will be included in the discussion segment of the research; while, other results (tables, charts, and graphs) will be added to the appendix. Weka is a powerful analytical tool that can generate a wide range results through the use of in-built statistical analysis algorithms. Microsoft Excel is a user-friendly software that allows for easy compilation and evaluation of data sets. The descriptive statistics (e.g. mean, Standard deviation, and variance) of the data will be compiled together; moreover, regression analysis be performed to clarify relationships between different variables. A hypothesis analysis maybe included for data variables with considerably similar results and outputs. Hypothesis will be employed (if necessary) to answer question about the association between variable statistics; for instance, is the mean for age-adjusted death rate equal for both men and women.
Dataset 1
It is important to note that the following variable identities were given by Weka to the 18 variables; which are influenced by race and sex factors with regard to the life expectancy and death rate in the dataset.
Indicated Variable |
Meaning |
AverageAllBoth |
Average Life Expectancy: All Races for Both Gender |
AverageAllFem |
Average Life Expectancy: All Races for Females |
AverageAllMal |
Average Life Expectancy: All Races for Males |
AverageBlackB |
Average Life Expectancy: Black Race for Both Gender |
AverageBlackF |
Average Life Expectancy: Black Race for Females |
AverageBlackM |
Average Life Expectancy: Black Race for Males |
AverageWhiteB |
Average Life Expectancy: White Race for Both Gender |
AverageWhiteF |
Average Life Expectancy: White Race for Females |
AverageWhiteM |
Average Life Expectancy: White Race for Males |
AgeadjAllBot |
Aged-adjusted Death Rate: All Races for Both Gender |
AgeadjAllFem |
Aged-adjusted Death Rate: All Races for Females |
AgeadjAllMal |
Aged-adjusted Death Rate: All Races for Males |
AgeadjBlackB |
Aged-adjusted Death Rate: Black Race for Both Gender |
AgeadjBlackF |
Aged-adjusted Death Rate: Black Race for Females |
AgeadjBlackM |
Aged-adjusted Death Rate: Black Race for Males |
AgeadjWhiteB |
Aged-adjusted Death Rate: White for Both Gender |
AgeadjWhiteF |
Aged-adjusted Death Rate: White Race for Females |
AgeadjWhiteM |
Aged-adjusted Death Rate: White Race for Males |
Descriptive statistics for dataset specified above are as follows in Weka.
Variable |
Mean |
Median |
Minimum |
Maximum |
AverageAllBoth |
66.547 |
69.6 |
39.1 |
78.9 |
AverageAllFem |
69.199 |
72.9 |
42.2 |
81.3 |
AverageAllMal |
64.016 |
66.6 |
36.6 |
76.5 |
AverageBlackB |
58.355 |
63.6 |
30.8 |
75.6 |
AverageBlackF |
60.963 |
66.1 |
32.5 |
78.5 |
AverageBlackM |
55.789 |
60.5 |
29.1 |
72.5 |
AverageWhiteB |
67.34 |
70.5 |
39.8 |
79.1 |
AverageWhiteF |
70.044 |
73.9 |
43.2 |
81.4 |
AverageWhiteM |
64.803 |
67.4 |
37.1 |
76.7 |
AgeadjAllBot |
1477.9 |
1336.5 |
724.6 |
2541.6 |
AgeadjAllFem |
1305.1 |
1113.6 |
616.7 |
2410.4 |
AgeadjAllMal |
1682.7 |
1611.7 |
855.1 |
2740.5 |
AgeadjBlackB |
1881 |
1561.3 |
849.3 |
3586.2 |
AgeadjBlackF |
1694.5 |
1336.2 |
710.8 |
3362.4 |
AgeadjBlackM |
2112.9 |
1861.1 |
1034 |
3845.7 |
AgeadjWhiteB |
1446.9 |
1310.2 |
725.4 |
2501.2 |
AgeadjWhiteF |
1275.2 |
1085.8 |
617.6 |
2394 |
AgeadjWhiteM |
1650.5 |
1587.3 |
853.4 |
2680.7 |
Variable |
Std. Dev. |
|||
AverageAllBoth |
9.631 |
|||
AverageAllFem |
10.161 |
|||
AverageAllMal |
9.0355 |
|||
AverageBlackB |
13.113 |
|||
AverageBlackF |
14.072 |
|||
AverageBlackM |
12.117 |
|||
AverageWhiteB |
9.563 |
|||
AverageWhiteF |
10.042 |
|||
AverageWhiteM |
9.0227 |
|||
AgeadjAllBot |
553.98 |
|||
AgeadjAllFem |
569.5 |
|||
AgeadjAllMal |
520.25 |
|||
AgeadjBlackB |
780.51 |
|||
AgeadjBlackF |
822.3 |
|||
AgeadjBlackM |
716.99 |
|||
AgeadjWhiteB |
545.14 |
|||
AgeadjWhiteF |
559.6 |
|||
AgeadjWhiteM |
512.95 |
Looking at the Mean for average life expectancy; it is clear that white females have the highest life expectancy while black males have the lowest. The mean for age-adjusted death rate we see that black males have the highest figure and the lowest is taken by white females. Overall using the minimum and maximum statistics it is easy to observe that black males have the lowest life expectancy ever documented within the 115 year period; while, white women have the highest life expectancy between 1900 and 2015. In addition, the greatest figure for age-adjusted death rate was taken up by black males while the minimum number of deaths was witness in females from both races. The average life expectancy data for all variables is negatively skewed; on the other hand, age-adjusted death rate data for all 9 variables is positively skewed.
The graph above indicates average life expectancy for all races and gender groups. The general trend is that average life expectancy has increased substantially for all individuals between 1900 and 2015. It as showcases the age-adjusted death rate for all individuals regardless of race or gender. The overall feel in the movement of the lines indicates that age-adjusted death rate has decrease significantly over the past 115 year for all race and both gender groups.
The correlation matrix below is for all average life expectancy variables. The correlation between all variables is positive and very strong. However, there are those with stronger correlation with each compared to others; for instance, the correlation between the average life expectancy data for black males and all females can be considered the weakest. Nevertheless, all nine variables have strong associations with each other.
AverageAllBoth |
AverageAllFem |
AverageAllMal |
AverageBlackB |
AverageBlackF |
|
1 |
0.9977 |
0.9975 |
0.992 |
0.9922 |
AverageAllBoth |
1 |
0.9906 |
0.9911 |
0.9944 |
AverageAllFem |
|
1 |
0.9887 |
0.9854 |
AverageAllMal |
||
1 |
0.9981 |
AverageBlackB |
|||
1 |
AverageBlackF |
||||
AverageBlackM |
AverageWhiteB |
AverageWhiteF |
AverageWhiteM |
||
0.9864 |
0.9994 |
0.9971 |
0.9965 |
AverageAllBoth |
|
0.9822 |
0.997 |
0.9992 |
0.9895 |
AverageAllFem |
|
0.9871 |
0.9972 |
0.9904 |
0.9994 |
AverageAllMal |
|
0.9973 |
0.9919 |
0.9914 |
0.9879 |
AverageBlackB |
|
0.9909 |
0.9915 |
0.9937 |
0.984 |
AverageBlackF |
|
1 |
0.9874 |
0.984 |
0.9871 |
AverageBlackM |
|
1 |
0.9977 |
0.9975 |
AverageWhiteB |
||
1 |
0.9906 |
AverageWhiteF |
|||
1 |
AverageWhiteM |
The correlation matrix below shelters all variables for age-adjusted death rate. All 9 variables have strong positive correlation. Amongst these the “weakest” correlation is between white males and black females. A correlation matrix of all 18 variables indicates there is a strong negative correlation between age-adjusted death rate variables and average life expectancy variables.
AgeadjAllBot |
AgeadjAllFem |
AgeadjAllMal |
AgeadjBlackB |
AgeadjBlackF |
|
1 |
0.9966 |
0.9928 |
0.9905 |
0.9899 |
AgeadjAllBot |
1 |
0.9799 |
0.9921 |
0.9956 |
AgeadjAllFem |
|
1 |
0.979 |
0.9716 |
AgeadjAllMal |
||
1 |
0.9976 |
AgeadjBlackB |
|||
1 |
AgeadjBlackF |
||||
AgeadjBlackM |
AgeadjWhiteB |
AgeadjWhiteF |
AgeadjWhiteM |
||
0.9792 |
0.9997 |
0.9958 |
0.9924 |
AgeadjAllBot |
|
0.9762 |
0.9966 |
0.9997 |
0.9795 |
AgeadjAllFem |
|
0.9765 |
0.9921 |
0.9786 |
0.9996 |
AgeadjAllMal |
|
0.9946 |
0.9906 |
0.9922 |
0.9782 |
AgeadjBlackB |
|
0.9853 |
0.9901 |
0.9958 |
0.971 |
AgeadjBlackF |
|
1 |
0.9791 |
0.9764 |
0.9754 |
AgeadjBlackM |
|
1 |
0.9964 |
0.9923 |
AgeadjWhiteB |
||
1 |
0.9788 |
AgeadjWhiteF |
|||
1 |
AgeadjWhiteM |
The X-Y scatter plot below takes into consideration that average life expectancy (for all races and both sexes) is on the X-axis and age-adjusted death rate (for all races and both sexes) is on the y-axis. The best line of fit indicates that there is an inverse relationship between the two values: Where increment in one variable will result in a decrement in the other. Below the X-Y scatter plot is a table that contains the output for OLS estimation or regression analysis. We are using average life expectancy for all races and both sexes as the dependent variables and the independent variables are average life expectancy for all races males and females; hence there are two predictor variables (AverageAllFem and AverageAllMal) and one explanatory variable (AverageAllBoth).
Dataset 2
The results below were generated by analyzing the prevalence of these diseases will regard to summary statistics or descriptive statistics like mean, median, and variance. The results for all the other disease causes will be included in the appendix. Mean deaths attributed to cancer are considerably high as indicated below in the table.
All Causes |
Alzheimer’s Disease |
Cancer |
||||
Deaths |
Deaths |
Age-adjusted Death Rate |
Deaths |
Age-adjusted Death Rate |
||
Mean |
95409.0905 |
803.9563348 |
2844.59 |
24.24841629 |
21824.65611 |
181.1807692 |
Median |
37031 |
791.6 |
1088.5 |
23.7 |
8171.5 |
181.2 |
STD |
337913.683 |
96.97837913 |
10343.19 |
6.842249981 |
77292.59984 |
20.32010349 |
Variance |
1.14186E+11 |
9404.806019 |
1.07E+08 |
46.8163848 |
5974145990 |
412.906606 |
Skewness |
6.808841259 |
0.414801881 |
7.269754 |
0.419009826 |
6.795664801 |
-0.062327522 |
Maximum |
2712630 |
1087.3 |
110561 |
47.1 |
595930 |
241.4 |
Minimum |
2708 |
584.9 |
24 |
7 |
633 |
124.7 |
Range |
2709922 |
502.4 |
110537 |
40.1 |
595297 |
116.7 |
5% Percentile |
5050.7 |
663.145 |
126.15 |
14.315 |
1154.55 |
148.015 |
95% Percentile |
170777.8 |
981.34 |
4828.45 |
36.285 |
40050.8 |
212.685 |
The following is a correlation table for some of the cause in the dataset. There is a moderately strong correlation between the aged-adjusted death rate for all causes and that of cancer. Likewise, three is a very strong positive correlation between deaths linked to Alzheimer’s and all causes. However, majority of the data variables have weak negative correlation with each other.
All Causes |
Alzheimer’s Disease |
Cancer |
|||||
Deaths (AC) |
Age-adjusted Death Rate (AC) |
Deaths (AD) |
Age-adjusted Death Rate (AD) |
Deaths (C) |
Age-adjusted Death Rate (C) |
||
All Causes |
Deaths (AC) |
1 |
|||||
Age-adjusted Death Rate (AC) |
-0.032057555 |
1 |
|||||
Alzheimer’s Disease |
Deaths (AD) |
0.919625615 |
-0.045800368 |
1 |
|||
Age-adjusted Death Rate (AD) |
-0.035167414 |
-0.006130004 |
0.016974727 |
1 |
|||
Cancer |
Deaths (C) |
0.937767191 |
-0.02271747 |
0.977796089 |
-0.038233286 |
1 |
|
Age-adjusted Death Rate (C) |
-0.035476148 |
0.697064827 |
-0.050329853 |
-0.057645321 |
-0.015964134 |
1 |
The table below is a representation of regression analysis where the dependent variable is deaths associated with all causes; and the independent variables are deaths and age-adjusted death rates for both Alzheimer’s and Cancer. The adjust R square is considerably high at 87.94% and the significant of F is equivalent to zero. Deaths linked to both Alzheimer’s and cancer has a positive impact on the value of the dependent variables. On the other hand, age-adjusted death rates for both Alzheimer’s and cancer have a negative impact on the explanatory variable.
By taking a one year assessment of deaths and age-adjusted death rate, we are able to recognize the presence of outliners. This outliners are considerably large which means they have a significantly impact on any regression model devised for the purposes of prediction and estimation. If there is an assumption that states that the means for cancer and Alzheimer’s are equivalent across the 16 year interval. By performing a hypothesis analysis this statement can either be rejected or not reject.
H0 (null hypothesis): The means for Alzheimer’s and Cancer are equal i.e.
H1 (alternative hypothesis): The means for Alzheimer’s and cancer are not equal i.e.
Using the in-built assessment tool in Microsoft Excel for Z-test of means for two samples, we can assess the hypothesis to get the appropriate results. The assessment yielded the following findings. We will not reject the null hypothesis given the p-value of the Z-score is less than alpha (0.05). As such, we do not reject that the death means for Alzheimer’s and cancer are equal.
z-Test: Two Sample for Means |
||
Deaths(Alzheimer’s) |
Deaths(Cancer) |
|
Mean |
2844.590498 |
21824.65611 |
Known Variance |
106981483.1 |
5974145990 |
Observations |
884 |
884 |
Hypothesized Mean Difference |
0 |
|
z |
-7.236553684 |
|
P(Z<=z) one-tail |
2.30149E-13 |
|
z Critical one-tail |
1.644853627 |
|
P(Z<=z) two-tail |
4.60298E-13 |
|
z Critical two-tail |
1.959963985 |
From the findings of data set 1 we can make the following observations. The fact that black males have the lowest average life expectancy and considerably high age-adjusted death rate indicates that they facing numerous hardships that put their lives at risk. Contrary to this, white females have a very high average life expectancy and significantly low age-adjusted death rate. This indicates that this group of the American population is well protected and sheltered from situation, events, and occurrences that would put their lives at risk or lead to death. The lowest ever recorded average life expectancy was roughly 29 years which was observed amongst black males. This means at a given time in the past 115 years ; black men were exposed to so many challenges that it was difficult for a significant proportion of them to make it into their thirties. On the opposite extreme, the highest ever documented average life expectancy was roughly 81.4 years amongst white females. In this case, we see that Caucasian women at some point in the past century were privileged enough to live to the ripe old age of eighty.
It is no surprise that the highest age-adjusted death rate ever recorded according to the data is associated with black males. This is expected given the fact that they have the lowest average life expectancy. Similarly, the fact that the group with the lowest age-adjusted death rate is that of all females in the United States of America disregarding race is expected give the role played by women in the past century. Women were often restricted from working dangerous jobs or were force to stay home to raise children where it was safe. Majority of the deaths that followed men were mostly influenced by racial tension, wars, and hostile working conditions. According to the analysis finding 95% of black men do not live to see the age of 71. Which is ten and five years shorter compared to that of white women and white men respectively. The time series plot for the average life expectancy data indicates improvement in longevity of life for individuals of all races. This could be as a result of advancement in healthcare, improved nutrition, better working conditions, reduced war campaigns, and overall socio-economic stability. The graph does however illustrate that black men still have the lowest life expectancy because of gang related activities, police brutality, drug-related conflict, and poor quality of life.
The graph for age-adjusted death rate indicates a reduction across the board for all individual. Nevertheless, black males still hold the highest age-adjusted death rate as indicated by their graph line. The death rate amongst females still remains considerably low compared to the other groups indicating a distinction between the activities performed by men and women. This is to mean that women tend to stay away from activities that put their lives in danger e.g. sky diving, paragliding, and mining. The correlation findings are very informative they prove that all population were to a degree subjected to the same social, political, and economic situations with only minute differences. As such, we do not see an increment in women death being accompanied by a decrement in male deaths. There is however an inverse relationship between average life expectancy and age-adjusted death rate. When individuals are put in situations and provided with means that allow them to better their quality of life they will undoubtedly increase their life expectancy which will in turn diminish age-adjusted deaths. Lately we can conclude based on our regression analysis; that an increment in the average life expectancy of women and men or either party will positive impact that of the entire population.
From the findings of data set 2, we can see that diseases of the heart are responsible for majority of the mean deaths observed in the United States of America between 1999 and 2015. This could be as a result of poor nutrition habits or increased causative agents in the localities of susceptible Americans. The second highest cause of deaths is cancer, with average figures of above 21,000. More and More people in the United States of America are being diagnosed with cancer. This has led people to believe that the ailment is tried in with nutrition, quality of water, proximity to industrial plants, and usage of some modern gadgets. Deaths associated with unintentional injuries are considerably indicating increased carelessness and disregard for human life amongst the American population. The results of the correlation matrix of all the diseases (in appendix) indicate that Deaths for different disease causes has strong positive correlation with each other. As such, an increment in Cancer deaths will be accompanied by increment in Alzheimer deaths. Aged-adjusted death rates for different disease cause have very weak positive correlations with each other; so much so, that their relationship can be ignore. Likewise a very weak negative correlation is observed between deaths and age-adjusted death rate between different diseases.
The regression analysis proves that the death figure of one disease (Alzheimer’s) can be used to predict another disease’s deaths numbers. The regression model used to assess this assumption showed that the model was significant at alpha equivalent to 0.05; moreover, the adjusted R square was considerably large. This implies that 87% of the values of the explanatory variable can be predicted using the independent variable. It is however necessary to mention that the presence of outliners does indeed damage the reliability and accuracy of these regression models. The hypothesis test did not affirm that the means of the two (cancer and Alzheimer’s) were equal but laid a basis that they were not significantly different. As such, this finding provides a foundation on which to assess whether there is significant correlation between the two diseases.
Based on the findings from data set 1, I would advocate for the empowerment of black males through provision of quality education, access to affordable healthcare, and opportunities to work high paying jobs. By so doing, numerous individuals will be turned away from activities that led to gang related violent, unemployment, and considerable interactions with law enforcement agencies. Moreover, the government can streamline policies in place to better the lives of black people without stripping away resources from white people. This ensures that both racial groups enjoy a win-win situation that will foster peace coexistence. Lately, I propose for the improvement of gender roles through the presentation of job recruitment opportunities to all individuals regardless of gender or race. Women are still shielded from undertaking in given activities simple because they are predominately performed by men. One major recommendation I would make with regards to results presented through the analysis of data set 2; would have to be the increment of awareness campaigns to educate people on the dangers of heart related complication and informative school programs to teach kids on everyday habits and activities that put them at risk of developing heart diseases in future.
Reference List
Rajendar Kumar, Research Methodology (New Delhi: APH Publishing, 2008), 34–120.
Debra Wetcher-Hendricks, Analyzing Quantitative Data: An Introduction for Social Researchers (Hoboken: John Wiley & Sons, 2011), 1–398.
Sarah E. Kemp, Joanne Hort, and Tracey Hollowood, Descriptive Analysis in Sensory Evaluation (Hoboken: John Wiley & Sons, 2018), 594–744.
Ning-Zhong Shi, and Jian Tao, Statistical Hypothesis Testing: Theory and Methods (Singapore: World Scientific, 2008), 1–307.
Frederic P. Miller, Agnes F. Vandome, and John McBrewster, Statistical Hypothesis Testing (Saarbrücken: VDM Publishing, 2009), 1–102.
Leonard Gaston, Hypothesis Testing Made Simple (New York: Leonard Gaston Ph.D, 2014), 1–167.
Douglas C. Montgomery, Elizabeth A. Peck, and G. Geoffrey Vining, Introduction to Linear Regression Analysis (Hoboken: John Wiley & Sons, 2012), 1–645.
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