Activity 36

MATH 216: Statistical Thinking

Activity 1: Think-Pair-Share

Consider an experiment designed to estimate the linear relationship between the percentage of a certain drug in the bloodstream of a subject and the length of time it takes the subject to react to a stimulus. In particular, the researchers want to predict reaction time \(y\) based on the amount of drug in the bloodstream \(x\). Data were collected for five subjects, and the results are shown in Table 11.1. (The number of measurements and the measurements themselves are unrealistically simple in order to avoid arithmetic confusion in this introductory example.)

  1. Use the method of least squares to estimate the values of \(\beta_0\) and \(\beta_1\).
  1. Predict the reaction time when \(x=2\).
  1. Find the SSE for the analysis.
  1. Give practical interpretations of \(\widehat{\beta}_0\) and \(\widehat{\beta}_1\).

Activity 2: Group Activities with Real Data

  1. Task: Use the provided dataset (study hours and GPA) to calculate the correlation, slope, and intercept of the regression line.
  2. Interpretation: Discuss what these parameters tell you about the relationship between study hours and GPA.