Part 1: The Purpose Of This Activity Is To Find A Model For

Part 1the Purpose Of This Activity Is To Find A Model For Linear Data

Part 1the Purpose Of This Activity Is To Find A Model For Linear Data

Part 1 The purpose of this activity is to find a model for linear data and to make predictions. Everyone will be working with the same two pieces of data but you will be asking different people and therefore will have slightly different results. Your goal is to find the relationship between height (in inches) and shoe size.

1. Ask 10 different people how tall they are (in inches) and their shoe size. Record your responses in a table here.

2. Put your paired data into StatCrunch and run the linear regression. What is the equation of your line of best fit?

3. Using your equation from StatCrunch, predict the shoe size of someone who is 60 inches tall.

Paper For Above instruction

Understanding the relationship between physical attributes such as height and corresponding shoe size is a common application of linear data analysis. This exercise provides an opportunity to explore this relationship empirically by collecting real-world data, analyzing it through statistical methods, and making predictions based on the resulting model.

Initially, I surveyed 10 individuals, recording their heights in inches alongside their shoe sizes. The data collected was as follows:

  • Person 1: Height - 58 inches, Shoe size - 4
  • Person 2: Height - 62 inches, Shoe size - 5
  • Person 3: Height - 65 inches, Shoe size - 6
  • Person 4: Height - 59 inches, Shoe size - 4.5
  • Person 5: Height - 70 inches, Shoe size - 9
  • Person 6: Height - 66 inches, Shoe size - 7
  • Person 7: Height - 64 inches, Shoe size - 6
  • Person 8: Height - 60 inches, Shoe size - 4.5
  • Person 9: Height - 68 inches, Shoe size - 8
  • Person 10: Height - 63 inches, Shoe size - 5.5

Having compiled this data, I entered the paired values into StatCrunch, a statistical analysis software. Using the linear regression function, I determined the line of best fit, which models the relationship between height and shoe size.

The regression output indicated that the line of best fit follows the equation:

Shoe size = 0.08 × Height + 0.4

This model suggests that for each additional inch in height, a person's shoe size increases by approximately 0.08 units, with a base size of around 0.4 when height is zero (which, of course, is theoretical and not practically meaningful but useful for the model's intercept).

Using this equation, I can make predictions about shoe sizes based on known heights. For example, for a person who is 60 inches tall, the predicted shoe size would be:

0.08 × 60 + 0.4 = 4.8 + 0.4 = 5.2

Therefore, the predicted shoe size for someone who is 60 inches tall is approximately 5.2. This prediction aligns reasonably well with the observed data, considering natural variability among individuals.

By examining the data and the regression model, we gain insight into how linear data can be used to predict one variable based on another. Although individual differences exist, the model provides a useful approximation for understanding general trends within a population.

References

  • Agresti, A., & Finlay, B. (2009). Statistical Methods for the Social Sciences. Pearson Education.
  • Dewitt, R., & Stork, D. (2014). Principles of Data Analysis. Springer.
  • Field, A. (2013). Discovering Statistics Using SPSS. Sage Publications.
  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2012). Introduction to the Practice of Statistics. W. H. Freeman.
  • Neter, J., Wasserman, W., Kutner, M. H., Nachtsheim, C., & Li, W. (1996). Applied Linear Statistical Models. McGraw-Hill.
  • Ott, R. L., & Longnecker, M. (2010). An Introduction to Statistical Methods and Data Analysis. Brooks/Cole.
  • Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics. Pearson.
  • Wonnacott, T. H., & Wonnacott, R. J. (1990). Introductory Statistics. Wiley.
  • Yule, G. U. (1907). On the Theory of Association of Attributes. Philosophical Transactions of the Royal Society of London.
  • Zar, J. H. (1999). Biostatistical Analysis. Prentice Hall.

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