Statistics
Bivariate Analysis
This project will be done in a group of no more than three. You may distribute the work as you see fit. Your project will be evaluated based on standards which will be available prior to the presentations.
- Obtain a set of data with at least two quantitative variables (n>30) that are good candidates for regression analysis.
- Perform univariate analysis of each variable
- Vital Stats (x-bar, s, 5# summary, etc.).
- Do the “outlier test”
- Assess Normality
Histogram (shape, outliers identified and discussed)
Empirical Rule Test
- Identify an explanatory and a response variable for your focus and explain the reason for your designation of each.
- Produce a high-quality scatterplot of your data (use your calculator and a graph link, statistical software on a computer, or other comparable tools). Discuss the overall pattern of the scatterplot (including a discussion of form, direction, and strength) and outliers that may be present. If there are any categorical variables present, identify the categories in some obvious manner on the graph.
- Draw the regression line on a second scatterplot and state its equation.
- Discuss each of the following in detail:
- The meaning of the slope (marginal change) of the regression line
- How and why you would, or would not, use this equation to predict values of the response variable.
- The value of the correlation coefficient and what it means in relation to your data.
- The total variation, explained variation, and unexplained variation; the coefficient of determination and what these mean in relation to your data.
- The standard error of estimate
- Construct a 95% prediction interval for y given that x = ____ (you choose x; must fall within the values of your data for x). This will provide a sense of how accurate a predicted value of x = _____ really is.
- Produce a high-quality residual plot and discuss the information it gives you about the linearity of your data.
- Write up your findings (Introduction, Analysis, Conclusion) in a detailed PowerPoint (or video).
- Make an oral presentation of your results. All graphs and interpretations should be illustrated. The visual aides should “tell the story” of your data.
- For bonus consideration, discuss and illustrate how transformations of your data affect the regression equation and the correlation coefficient (see section 10-6: Modeling).
Statistics
Correlation – Regression – Etc.
The following are potential relationship/correlation studies. They are intentionally somewhat vague to promote thought. Many of them can also be considered visa-versa, but be careful in denoting the response and explanatory variables. Feel free to come up with your own (I love creativity)!
Give me your group names and correlation/regression topic ASAP – there is to be no repetition between projects or periods. The first group to pick a topic gets it!
- Is there a correlation between Ch.1 test scores and Ch.2 test scores?
- Is there a correlation between GPA and SAT scores?
- Is there a correlation between SAT math and SAT verbal?
- Is there a correlation between hours worked/week and GPA?
- Is there a correlation between parent’s income and student’s GPA?
- Is there a correlation between parent’s income and student’s SAT scores?
- Is there a correlation between time of the day and memory ability?
- Is there a correlation between time of the day and alertness?
- Is there a correlation between time of the day and blood pressure?
- Is there a correlation between student’s income and his/her car value?
- Is there a correlation between time and the distance an object falls?
- Is there a correlation between age and weight?
- Is there a correlation between age and height?
- Is there a correlation between height and weight?
- Is there a correlation between a car’s weight and its fuel economy?
- Is there a correlation between height and weight?
- Is there a correlation between a car’s weight and its fuel economy?
- Is there a correlation between cricket chirps and temperature?
- Is there a correlation between the number of guns/capita and the number of murders/capita?
- Is there a correlation between IQ and GPA?
- Is there a correlation between the number of rounds of golf played and the score?
- Is there a correlation between GPA and unemployment rates?
- Is there a correlation between the number of statistics homework problems completed and the average score?