Project 2: Regression
Due date: December 17.
Generate individual dataset by following instructions in the Regression Project notebook.
Perform visual analysis of the data and investigate the relationship by constructing a scatter plot. Summarize findings.
Construct a linear regression model of your sample data.
Select 10% sample by picking every 10th value from the population and perform inference analysis calculations:
Confidence interval of the slope
Confidence interval for the mean of responses
Submit your report, as PDF document, with results of visual data and regression analysis, as well as inference results for the selected dataset.
INCLUDE HASH AND GENERATED POPULATION DATASET (predictors and response points) INTO YOUR REPORT
Below is a detailed outline of the content that could be included in your project report. The components are listed in outline form so that they can be used as a checklist. However, your project report is expected to be a formal paper (not an outline). Your results should be stated in complete sentences, and your paper should be written in paragraph form. Although you may choose to use headings, you should not number your paragraphs.
Introduction. State the topic of your study as a research question and/or as a specific hypothesis to be tested. For example, your hypothesis should indicate what type of correlation you expected to see (positive or negative) and how strong you expected the correlation to be (weak, moderate, strong). Your hypothesis should describe a specific result that you expected to find and the practical reason that you expected this result (your rationale).
Define Population. Define clearly the population(s) that you intend for your study to represent.
Define Variable(s). Define clearly the variable(s) that are analyzing.
Study Design. Identify statistical procedures you used to analyze your data. Give relevant design details (e.g., which variable was selected as the explanatory variable, and which the response variable? Why? What type of correlation did you expect? And so on.)
Results. Descriptive Statistics. You should give descriptive statistics for each of your two quantitative variables. Note that you will be reporting summary statistics for both your explanatory variable and your response variable. You could report each set of descriptive statistics using both a table and a chart as described below. All tables and charts should be placed directly in your report.
Table: Give sample size, mean, standard deviation, and a 5-number summary for each variable (minimum, first quartile, median, third quartile, and maximum).
Chart: Show boxplots that illustrates the distribution of each variable.
Results. Statistical Analysis. Report the results of your analysis; you could include following items:
Scatter plot with a graph of the regression line
Value of the correlation coefficient r and interpretation of its meaning
Equation of the regression line
An example of a prediction using the regression equation
Correlation value for the regression model and interpretation of its meaning
Findings. Interpret the results of your statistical analysis in the context of your original research question. Do your analyses support your expected findings? Explain.
Discussion. What conclusions, if any, do you believe you can draw as a result of your study? If the results were not what you expected, what factors might explain your results? What did you learn from your project about the population(s) your studied? What did you learn about the research variables? What did you learn about the specific statistical analysis you conducted?
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