## Problem Description:

The primary focus is on conducting a correlation analysis using statistical data. The problem statement revolves around the examination of the relationship between two continuous variables: the Second-Year OMM Written Examination score and the Complex-USA Level 1 Total Score. Students are required to assess the strength and significance of this correlation, interpret its implications, and perform regression analysis. Additionally, students must analyze a case study involving the prediction of standardized test scores using GPA. The aim is to evaluate students' understanding of correlation analysis, regression, and data interpretation in a real-world context, ultimately demonstrating their ability to apply statistical concepts to practical scenarios.

## Solution

**CORRELATION ANALYSIS:
**

**Statistical Association: **Statistical Association describes the relationship between what types of variables?

** Ans:** Continuous Variables

## Use the figure below for next six questions

**Independent Variable & Scale of Measurement: **What is the independent variable & its scale of measurement? Ans: The independent variable is the Second-Year OMM Written Examination score, measured at an Interval scale.

**Dependent Variable & Scale of Measurement: **What is the dependent variable & its scale of measurement? Ans: The dependent variable is the Complex-USA Level 1 Total Score, measured at an Interval scale.

**r Value & Interpretation: **What is the r value? What does it tell us? Ans: The r-value is 0.53, indicating a moderate linear association between the Second-Year OMM Written Examination score and Complex-USA Level 1 Total Score. The correlation suggests that as the OMM score increases, the Complex-USA Level 1 Total Score also tends to increase.

**r2 Value & Interpretation: **What is the r2 value? What does it tell us? Ans: The r2 value is 0.28, indicating that 28% of the variation in the Complex-USA Level 1 Total Score can be explained by the Second-Year OMM Written Examination score.

**Predicting OMM Score:** Predict what OMM score is needed to obtain a COMLEX score of 600. Ans: An OMM score of 91.42 is needed to obtain a COMLEX score of 600 based on the provided model.

**Using COMLEX Scores to Predict OMM Score: **Should you use COMLEX scores to predict what a student’s OMM score was? Why or why not? Ans: No, COMLEX scores should not be used to predict a student's OMM score due to the poor performance of the model as indicated by the low r2 value.

**Decision Tree:** Regarding the Decision tree:

**Fill in any missing blanks**

**Ans:
**

- Comparing two or more quantitative variables
- Correlation and Regression
- 1 sample t-test
- Paired or related samples
- Independent student t-test, Confidence Intervals, or Mann-Whitney U-test

## Study Abstract:

**Variables: **What are the variables the study is looking at?

**Ans:** The variables studied are teaching evaluation scores, student’s final grades, and course fail rates.

**Correlation Analysis Assumptions:**

- What are the assumptions in conducting a correlation analysis?

**Ans:
**

- Both variables must be continuous.
- There should be no outliers in the variables.
- A linear relationship between the two variables must exist.

**Meeting Assumptions:**

- Did this study meet those assumptions, based on the abstract provided? Ans: Yes, the study met the assumptions.

**Causation Elements: **

- Describe the required elements for causation. Ans: Causation requires Temporal precedence, Empirical association, and Nonspuriousness to be satisfied.

**Study's Conclusion: **

- Did this study conclude that one variable caused another to occur? Ans: Yes, the study concluded that students’ final grades have an effect on the teaching evaluation scores.

**Results Table:
**

**Covariance Definition: **

**Define covariance:** Ans: Covariance is a measure of how two random variables in a data set change together.

**Variables for Covariance:** Based on the table and abstract provided earlier in the assignment, what are the two variables associated with covariance for this study? Ans: The variables associated with covariance are teaching evaluation scores and student’s final grades.

**r Value for 2014:** What is the r value for teaching evaluations linking to each student’s grade in 2014? Ans: The r value for 2014 is 0.080.

**Sign of Correlation Coefficient: **What does the sign of this correlation coefficient indicate in relation to the study and abstract? Ans: The positive sign indicates a positive correlation between teaching evaluation scores and students’ final grades in 2014.

**Statistical Significance:** Is the r value for teaching evaluation scores linked to whole class average grades statistically significant? If yes, what is the p value less than? Ans: Yes, the r value for teaching evaluation scores linked to whole class average grades is statistically significant with a p-value less than 0.001.

## Graph Analysis:

**Weakest Correlation: **

- Which graph below depicts the weakest correlation? Ans: Graph C depicts the weakest correlation.

**Strongest Correlation:**

- Which graph below depicts the strongest correlation? Ans: Graph A depicts the strongest correlation.

**Graph A's Correlation: **Is graph A depicting a positive or negative correlation? Ans: Graph A depicts a positive correlation.

## REGRESSION ANALYSIS:

**Comparison of Regression Types: **Compare and contrast simple linear regression, multiple regression, and logistic regression. Ans: (Explanation provided)

Main Symbol for Regression Output: What is the main symbol for output of regression analysis and what does it tell us? Ans: The main symbol is Y, representing the value for each respective observation.

**Simple Linear Regression Formula:** List the formula for simple linear regression and describe what each variable stands for. Ans: (Formula and explanation provided)

## CASE STUDY (USE EXCEL):

**Calculating r: **Calculate the value of r using Excel. Ans: The r value is 0.524.

**Interpreting r: **Interpret the value of r in terms of the hypothesis. Ans: The value indicates a moderate linear relationship between achievement test scores and class performance.

**Predicting Test Score:** If you wanted to predict a student’s standardized test score using their GPA, what statistical analysis would you use? Ans: Regression Analysis

**Intercept and Slope: **To get the y-intercept and slope, use Excel. Ans: (Values provided)

**Predicted Test Score:** Insert the values into the equation and determine what test score is expected if a student has a GPA of 3.8. Ans: (Calculation and answer provided)

**R2 Calculation: **What proportion of variation in standardized test scores is explained by GPA? What is the R2 value? Ans: (R2 value and interpretation provided)

Scatterplot: Using Excel, create a scatterplot of the case study data. Ans: (A screenshot is required.)