Exploring Relationships Between Two Variables
Project 2: Exploring relationships between two variables In this project, you will search two quantitative variables that may have a linear association. You will describe and analyze the relationship between the variables the way it is explained in Chapter 4 (4.1-4.2). Then, you will create a written report including all 4 parts below and turn in by the stated due date according to the guidelines provided in this paper. Required components: 1. Understand the Problem Find data that includes two quantitative variables that may have a linear association. You can find the data from the internet or any other media a) You may use the student data from this website: Student data b) Or you can find your own data. List the website where you found the data. c) Before you even analyze the data, use your intuition and/or experience to make a prediction about the possible relationship. • Do you think there will be an association? If so, will it be positive or negative? • Do you expect a strong or weak association? Why? Next, develop a question that address a possible linear association between two variables. d) What are the two variables from the data that are relevant to answer the questions: e) State the question(s) you are interested in testing: 2. Analyze the paired Data a) What one of the variables is the likely explanatory variable and which is the response variable? b) Draw a scatter diagram of the data. Does the graph show a linear relationship between the two variables? Comment on the direction and strength that appears on the scatter diagram. c) Compute the linear correlation coefficient between the two variables and interpret the meaning specifically for your data. Use the list of critical values (see below) to determine whether you have enough data to make any claims based on the coefficient obtained. If not, then you may want to consider collecting more data. i. What is the correlation coefficient? ii. What is the critical value? iii. Based on these two numbers, is there a linear association? d) Find the equation of the least-squares regression line. e) Interpret the slope and write a sentence explaining what it tells you. f) Interpret the y-intercept and write a sentence explaining what it tells you g) Use the equation of the least-squares regression line to predict the outcome (y-value) for one of the x-values in your data. h) Find the residual for the x-value you chose in part (f). i. Is the residual positive or negative? ii. Which one has a large y-value, the prediction or the observation? 3. Draw Conclusions a) What do the results indicate about the relationship between two variables? b) Correlation doesn’t imply causation. With your data, do you think there is a causal relation between the variables? If so, why do you think that it goes beyond just a correlation? c) How did your expectation differ (or not differ) from the actual results? d) Write a short summary of the main findings that you discovered.
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