Activity 35

MATH 216: Statistical Thinking

Activity 1: Quiz

Question: Given the following data points for variables \(x\) and \(y\), calculate the correlation coefficient \(r\):
- \((x_1, y_1) = (2, 4)\)
- \((x_2, y_2) = (4, 8)\)
- \((x_3, y_3) = (6, 12)\)
- \((x_4, y_4) = (8, 16)\)
- \((x_5, y_5) = (10, 20)\)

Activity 2: Data Exploration

Make a scatter-plot and write the equation for the linear model.

Activity 3: Real Data Analysis

Recreate the scatterplot shown in the lecture and calculate the correlation coefficient for the following pairs of variables:

Horsepower vs. MPG (Miles Per Gallon)
Weight vs. MPG
Engine Size vs. Horsepower

Activity 4: Case Studies and Problem-Solving

Case Study: A health researcher is studying the relationship between the number of cigarettes smoked per day and lung capacity. The researcher collected data from 50 participants and found a correlation coefficient of \(r = -0.65\).

Question: What does this correlation coefficient suggest about the relationship between smoking and lung capacity?
Task: Using the linear regression model, predict the lung capacity for a person who smokes 10 cigarettes per day. Assume the regression equation is: \[ \hat{y} = 100 - 2x \] where \(x\) is the number of cigarettes smoked per day and \(\hat{y}\) is the predicted lung capacity.