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 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 rate11025214963165641595511236782711258174791014101916

Using the Minitab statistical procedure:

• Calculate Pearson's correlation coefficient.
• make 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.