*Project: Regression* *1. Problem Identification (5 marks)* 1.1 *Description*: A researcher wants to investigate the relationship between the number of hours studied and the exam scores of students. The researcher collects data on the number of hours studied and the corresponding exam scores. 1.2 *Brief Statement of Intent*: The intent of this project is to use regression analysis to model the relationship between the number of hours studied and exam scores. 1.3 *Main Idea or Topic*: Regression analysis to predict exam scores based on hours studied. 1.4 *Design Specification*: * The model should be able to predict exam scores based on the number of hours studied. * The model should be evaluated using statistical measures such as R-squared and mean squared error. *2. Investigations of Related Ideas (5 marks)* 2.1 *Investigations*: * *Investigation 1*: Research on simple linear regression and its application to real-world problems. + Merit: Provides a solid foundation for understanding the relationship between variables. + Demerit: May not account for non-linear relationships. * *Investigation 2*: Analysis of studies that have used regression analysis to predict academic performance. + Merit: Provides insights into the effectiveness of regression analysis in predicting academic performance. + Demerit: May not be directly applicable to this specific problem. *3. Generation of Ideas (10 marks)* 3.1 *Possible Solutions*: * *Solution 1*: Use simple linear regression to model the relationship between hours studied and exam scores. + Merit: Easy to implement and interpret. + Demerit: May not account for non-linear relationships. * *Solution 2*: Use polynomial regression to model the relationship between hours studied and exam scores. + Merit: Can account for non-linear relationships. + Demerit: May be more complex to implement and interpret. *4. Selection of Choice and Refinement (6 marks)* 4.1 *Indication of Choice*: Solution 1: Simple linear regression. 4.2 *Justification*: * Easy to implement and interpret. * Can provide a good fit for the data if the relationship is linear. 4.3 *Refinements*: * *Refinement 1*: Check for assumptions of linear regression, such as linearity and normality of residuals. * *Refinement 2*: Use R-squared and mean squared error to evaluate the model's performance. * *Refinement 3*: Consider transforming variables if necessary to improve the model's fit. 4.4 *Presentation*: A presentation will be made to showcase the results of the regression analysis. *5. Presentation of the Final Solution (10 marks)* 5.1 *Working Drawing*: A scatter plot with a regression line will be created to visualize the relationship between hours studied and exam scores. 5.2 *Artefacts*: The regression analysis will be presented, showcasing: * Quality: Accurate and well-interpreted results. * Functionality: Easy to understand and apply. * Fits and sizes: Suitable for the data. * Stability: Robust to changes in the data. * Relevance: Relevant to the research question. * Relevant tools: Use of statistical software or calculator. * Finish: Well-formatted and easy to read. * Symmetry: Balanced and logical structure. *6. Evaluation (5 marks)* 6.1 *Relevance to Brief*: The simple linear regression model addresses the research question and provides insights into the relationship between hours studied and exam scores. 6.2 *Problems Encountered*: One problem encountered was the potential for non-linear relationships between variables. 6.3 *Solution Suggested*: The solution was to check for assumptions of linear regression and consider transforming variables if necessary. 6.4 *Recommendations*: The model should be further refined and validated using additional data. Additionally, the results should be interpreted in the context of the research question and limitations of the study.