biostatistical methods 3

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• 1) Coefficient of Determination

  The purpose of this assignment is to learn about the coefficient of determination (R2) statistic as a measure of the fit of a regression line.R² is a statistical measure of how close the data are to a fitted regression line. In general, the higher the R², the better the model fits your data. However, while R² measures goodness of fit, it does not indicate whether a regression model is adequate. You can have a low R² value for a good model or a high R² value for a model that does not fit the data.Using the South University Online Library, the Internet, and your text readings, research about R².On the basis of your research and your involvement in public health functions, respond to the following:

  • Find and state a definition of R² that you feel is easy to understand.
  • In your own words, provide a substantive explanation of what R² represents.
  • Explain what the statistic R² is used for in regression analysis.
  • Explain how R² is affected by sle size.
  • Describe whether a large R² value means that a regression is significant. Provide reasons for your answer.
  • Describe how you would substantively interpret R².

• 2) Regression and Correlation Methods: Correlation, ANOVA, and Least Squares

  This is another way of assessing the possible association between a normally distributed variable y and a categorical variable x. These techniques are special cases of linear regression methods. The purpose of the assignment is to demonstrate methods of regression and correlation analysis in which two different variables in the same sle are related.The following are three important statistics, or methodologies, for using correlation and regression:

  • Pearson’s correlation coefficient
  • ANOVA
  • Least squares regression analysis

  In this assignment, solve problems related to these three methodologies.

  Part 1: Pearson’s Correlation Coefficient

  For the problem that demonstrates the Pearson’s coefficient, you will use measures that represent characteristics of entire populations to describe disease in relation to some factor of interest, such as age; utilization of health services; or consumption of a particular food, medication, or other products. To describe a pattern of mortality from coronary heart disease (CHD) in year X, hypothetical death rates from ten states were correlated with per capita cigarette sales in dollar amount per month. Death rates were highest in states with the most cigarette sales, lowest in those with the least sales, and intermediate in the remainder. Observation contributed to the formulation of the hypothesis that cigarette smoking causes fatal CHD. The correlation coefficient, denoted by r, is the descriptive measure of association in correlational studies.Table 1: Hypothetical Analysis of Cigarette Sales and Death Rates Caused by CHD

  State	Cigarette sales	Death rate
  1	102	5
  2	149	6
  3	165	6
  4	159	5
  5	112	3
  6	78	2
  7	112	5
  8	174	7
  9	101	4
  10	191	6

  Using the Minitab statistical procedure:

  • Calculate Pearson’s correlation coefficient.
  • Create a two-way scatter plot.

  In addition to the above:

  • Explain the meaning of the resulting coefficient, paying particular attention to factors that affect the interpretation of this statistic, such as the normality of each variable.
  • Provide a written interpretation of your results in APA format.

  Part 2: ANOVA

  Let’s take hypothetical data presenting blood pressure and high fat intake (less than 3 grams of total fat per serving) or low fat intake (less than 1 gram of saturated fat) of an individual.Table 2: Blood Pressure and Fat Intake

  Individual	Blood Pressure	Fat Intake
  1	135	1
  2	130	1
  3	135	1
  4	128	0
  5	121	0
  6	133	0
  7	145	1
  8	137	1
  9	148	1
  10	134	0
  11	150	0
  12	121	0
  13	117	1
  14	128	1
  15	121	0
  16	124	1
  17	132	0
  18	121	0
  19	120	0
  20	124	0

  Using the Minitab statistical procedure:

  • Calculate a one-way ANOVA to test the null hypothesis that the mean of each group is the same.
  • Use different variables as grouping variables (fat intake high 1; fat intake low 0) and compare the results.
  • Calculate an F-test for an overall comparison of means to see whether any differences are significant.

  In addition, in a Microsoft Word document, provide a written interpretation of your results in APA format.Visit the media Resources: One-Way ANOVA on lecture Correlation and Regression Methods to view an exle of ANOVA.

  Part 3: Least Squares
  The following are hypothetical data on the number of doctors per 10,000 inhabitants and the rate of prematurely delivered newborns for different countries of the world.Table 3: Number of Doctors Verses the Rate of Prematurely Delivered Newborns

  Country	Doctors per 100,000	Early births per 100,000
  1	3	92
  2	5	88
  3	5	85
  4	6	86
  5	7	89
  6	7	75
  7	7	70
  8	8	68
  9	8	69
  10	10	50
  11	12	45
  12	12	41
  13	15	38
  14	18	35
  15	19	30
  16	23	6

  Using the Minitab statistical procedure:

  • Apply least squares analysis to fit a regression line to the data.
  • Calculate an F-test and a t-test to test for the significance of the regression.
  • Test for goodness of fit using R2.

  In addition, in a Microsoft Word document, provide a written interpretation of your results in APA format.

 

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