Activity 37

MATH 216: Statistical Thinking

Activity 1: Quiz

  • Question: What does \(s\) represent in the context of linear regression?

      1. The slope of the regression line
      1. The typical error from predicted values
      1. The intercept of the regression line
      1. The variance of the predictor variable

Activity 2: Data Exploration

  1. Visualize the data using a scatter plot.
  2. Fit a linear model and interpret the coefficients.
  3. Check the assumptions of linear regression using diagnostic plots.
  4. Formulate the null and alternative hypotheses.
  5. Perform a t-test to check the significance of the slope.
  6. Interpret the results and discuss the implications for the relationship between \(x\) and \(y\).

Activity 3: Case Studies and Problem-Solving

  • Case Study: A study on the relationship between hours studied and exam scores. The dataset includes hours studied (x) and exam scores (y).

    1. Fit a linear model to the data.
    2. Check the assumptions of linear regression.
    3. Perform a hypothesis test on the slope and interpret the results.
    4. Discuss how the findings might influence study strategies.