InstructionsWeek 4: Project AssignmentRegression and Correlation Methods: Correlation, ANOVA, and Least SquaresThis is another way of assessing the possible association between a normally distributed

Instructions

Week 4: Project Assignment

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 sample 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

StateCigarette salesDeath rate

11025

21496

31656

41595

51123

6782

71125

81747

91014

101916

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.

Refer to the Assignment Resources: Dot Plots and Correlation and Resources: Performing Regression Analysis to view an example of Pearson's correlation coefficient. This same resources are also available under lecture Correlation and Regression Methods.

Submission Details:

• Name your Minitab output file SU_PHE5020_W4_A2a_LastName_FirstInitial.mtw.
• Name your document SU_PHE5020_W4_A2b_LastName_FirstInitial.doc.
• Submit your document to the Submissions Area by the due date assigned.

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

IndividualBlood PressureFat Intake

11351

21301

31351

41280

51210

61330

71451

81371

91481

101340

111500

121210

131171

141281

151210

161241

171320

181210

191200

201240

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 example of ANOVA.

Submission Details:

• Name your Minitab output file SU_PHE5020_W4_A2c_LastName_FirstInitial.mtw.
• Name your document SU_PHE5020_W4_A2d_LastName_FirstInitial.doc.
• Submit your document to the Submissions Area by the due date assigned.

Part 3: Least SquaresThe 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

CountryDoctors per 100,000Early births per 100,000

1392

2588

3585

4686

5789

6775

7770

8868

9869

101050

111245

121241

131538

141835

151930

16236

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.

Submission Details:

• Name your Minitab output file SU_PHE5020_W4_A2e_LastName_FirstInitial.mtw.
• Name your document SU_PHE5020_W4_A2f_LastName_FirstInitial.doc.
• Submit your document to the Submissions Area by the due date assigned.

Additional Materials

Dot Plots and Correlation

Performing Regression Analysis

Attachments