HW 07: Simple Linear Regression Modeling

All models are linear regression.

Purpose

Continue practicing bivariate analysis but creating a regression model, interpreting the coefficients, assess assumptions graphically and create predictions.

Submission instructions

  • Use the template provided: [QMD]
    • Right click and ‘save as’, then upload this file into your scripts folder in Posit Cloud.
  • Upload your PDF to Canvas by the due date

  1. State which variable (including the variable name from your codebook) will be your explanatory variable and which will be your response variable.

    • Think about the relationship among your variables, keeping in mind your original research questions. You may use gender as your categorical explanatory variable if you are struggling to find an explanatory and response relationship that makes sense.

  2. Create an appropriate bivariate plot to visualize the relationship you are exploring. Calculate appropriate summary statistics. Summarize the relationship between the explanatory and outcome variables in short paragraph form.

  3. Write the relationship you want to examine in the form of a research question.

    • Define the parameters being tested. (\(\beta_{1}\))
    • Translate the null and alternative hypotheses into \(H_{0}\) and \(H_{A}\) with symbols.

  4. Identify, justify, and fit the appropriate analysis.

    • State and verify assumptions of the test. Even if these assumptions are potentially violated, for the purposes of this assignment, acknowledge this limitation and continue with the prescribed analysis.
    • Fit the Ordinary Least Squares regression model. Extract the coefficients and corresponding confidence intervals.

  5. Interpret \(R^2\) and both \(\beta\) coefficients in context of the problem.

  6. Write a conclusion in context of the problem that includes a point estimate, confidence interval, and p-value.