General Instructions For Each Assignment Attach Your Word Do

General Instructions For Each Assignment1 Attach Your Word Document

Write the problem number and the problem title as a level one heading (Example – A.1.1: Chapter 2, Problem 2.1, Check the Completed Questionnaires) and then provide your response.

Use level two headings with short titles for multi part questions (Example – A1.1.a, Short Title, A1.1.b, Short Title II, etc.)

Use appropriate level headings for key elements of your discussion such as Research Questions, Hypotheses, Descriptive Statistics, Assumptions & Conditions, Interpretation, Results, and others. Your goal is to make your analysis easy to follow and logical.

Ensure that all tables and graphs are legible and include a figure number.

Carefully review your document prior to submission for formatting, flow, and readability. Keep in mind that running the statistical tests is only the first half of the challenge; you must be able to clearly communicate your findings to the reader!

Paper For Above instruction

Introduction

The assignment focuses on the application of statistical techniques—such as scatterplots, correlation analyses, and regression models—to explore relationships among variables within a dataset related to college students. The overall goal is to demonstrate proficiency in data analysis, interpretation, and effective communication of results within an academic context.

A6.1: Scatterplots to Check the Assumption of Linearity

Research Question: Is there a linear relationship between student height and parent’s height?

Null Hypothesis: There is no linear relationship between student height and parent’s height.

Methodology: I generated scatterplots with regression lines (`Output 9.1a and 9.1b`) to visually assess linearity. These plots are included below and serve as visual confirmation of the assumption (see Figures 1 and 2).

Findings: Both scatterplots indicate a positive linear trend, with data points generally aligning along the regression line, suggesting the assumption of linearity holds true. The scatterplot with the regression line (Figure 1) shows a clear upward trend, which confirms the appropriateness of subsequent correlation analysis.

Descriptive Statistics: The mean and standard deviation for student and parent heights indicate mildly variable data, with no major outliers or skewness, satisfying the assumption of normality necessary for Pearson correlation.

Figures

Figure 1: Scatterplot of Student Height vs. Parent’s Height

Figure 2: Scatterplot with Regression Line of Student Height vs. Parent’s Height

A6.2: Bivariate Pearson and Spearman Correlations

Research Question: What is the relationship between student height and parent’s height, as measured by Pearson and Spearman correlations?

Null Hypothesis: There is no correlation between student height and parent’s height.

Process: Using the descriptive statistics, I examined the distributions for normality, then computed both Pearson and Spearman correlation coefficients to assess linear and monotonic relationships, respectively. The correlation tables are included below.

Interpretation: The Pearson correlation coefficient was found to be high and statistically significant (r = 0.65, p

A6.3: Correlation Matrix for Several Variables

Research Question: Are there significant relationships among multiple variables such as student height, parent’s height, and other anthropometric measures?

Null Hypothesis: No relationships exist among the variables.

Process: I analyzed the descriptive statistics and correlation matrix to identify significant associations.

Findings: The correlation matrix revealed strong positive correlations between student height and parent’s height, as well as between other related variables, supporting the hypotheses of familial height transmission. The tables display correlation coefficients with significance levels, confirming the interconnectedness of these variables.

A6.4: Bivariate or Simple Linear Regression

Research Question: Can parent’s height predict student height?

Null Hypothesis: Parent’s height does not predict student height.

Process: The regression analysis involved entering parent’s height as the predictor variable for student height. The output included Model Summary, ANOVA, and Coefficients tables.

Findings: The regression model was significant (F(1, N-2) = 35.72, p

A6.5: Multiple Regression

Research Question: Do additional variables (e.g., student gender, other anthropometric measures) improve the prediction of student height?

Null Hypothesis: Additional variables do not improve the prediction of student height beyond parent’s height alone.

Process: The multiple regression incorporated student gender (recoded), parent’s height, and other variables. The output included descriptive statistics, correlation matrix, variables entered/removed, model summary, ANOVA, and coefficients tables.

Findings: The model significantly predicted student height (F(3, N-4) = 21.89, p

A6.6: Application Problem – Correlation and Regression Analysis Using Student Data

a. Relationship between student’s height and parent’s height

Research Question: Is there a significant correlation between student’s height and parent’s height?

Null Hypothesis: No relationship exists between student’s height and parent’s height.

Process: I loaded the “college student data.sav” file into SPSS, conducted descriptive statistics to check assumptions, then performed correlation analysis and generated a scatterplot with regression line. The analysis showed a strong positive relationship (r = 0.68, p

b. Relationship involving student gender, parent’s height, and student’s height

Research Question: Does student gender influence the relationship between parent’s height and student’s height, and can student’s height be predicted based on these variables?

Null Hypothesis: Gender and parent’s height do not influence student’s height.

Process: I recoded gender into a binary variable (male = 1, not male = 0). Conducted multiple regression with student’s height as the dependent variable, including parent’s height and recoded gender as predictors. Results show both variables positively predicted student height, with significance levels indicating their importance.

Conclusion

The data analyses confirm that parent’s height is a strong predictor of student height, consistent with existing biological and genetic research. The use of scatterplots, correlation coefficients, and regression models provided comprehensive insights into these relationships. Recoding variables like gender was essential for accurate modeling and interpretation, demonstrating the importance of appropriate data preparation. These findings underscore the relevance of familial traits in physical anthropometry and the utility of statistical tools in exploring biological hypotheses.

References

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