Lesson 6.1: Linear Association Between Two Numerical Variables
Software Lab 6.1
Scatterplots, Correlation, and Linear Relationships
Part of this software lab is adapted from Multiple Linear Regression (OpenIntro, n.d.-b) CC BY-SA 4.0 at OpenIntro Labs for jamovi.
As you work through the lab, answer the ungraded exercises in the shaded boxes. Check your answers by consulting the Software Lab 6.1 Solutions.
Remember to complete the graded Software Lab Questions for this section in Moodle.
Grading the Professor: The Data
Download evals_prof [CSV file] (OpenIntro, n.d.-a), which is a dataset gathered from end of semester student evaluations for 463 courses taught by a sample of 94 professors from the University of Texas at Austin. Load the data frame into jamovi. The variables we’ll be using in this lab are:
score: Average professor evaluation score across all courses taught by the professor: (1) very unsatisfactory – (5) excellent.bty_avg: Average beauty rating of professor based on ratings of the professors’ physical appearance by six students: (1) least attractive – (10) most attractive.age: Age of professor.
Before starting, go to the Data tab, double-click the column header for age, and change the Measure type from Nominal to Continuous.
Data Exploration
Analyses > Exploration > Descriptives, and move score, bty_avg, and age to the Variables box. Briefly summarize the variables numerically. Check your answer by consulting the Software Lab 6.1 Solutions.Descriptives dialog, select Plots > Histogram. Briefly describe the distributions of the variables.Scatterplots
Analyses > Exploration > scatr > Scatterplot, move bty_avg to the X-Axis box, and move score to the Y-Axis box. Briefly describe the appearance of the scatterplot. Does there appear to be a linear or curvilinear relationship between the variables? Are there any points that stick-out from the overall point cloud?Analyses > Exploration > scatr > Scatterplot, move age to the X-Axis box, and move score to the Y-Axis box. Briefly describe the appearance of the scatterplot. Does there appear to be a linear or curvilinear relationship between the variables? Are there any points that stick-out from the overall point cloud?Correlation
score and bty_avg, or between score and age?Analyses > Regression > Correlation Matrix, and move score, bty_avg, and age to the Variables box. Report Pearson’s correlations between score and bty_avg and between score and age, and confirm your answer for question 5.You should have identified two unusual points that stick-out in the scatterplots in questions 3 and 4. Go to the Data tab, click Filters, and type score>=3 in the 
box to remove those two data points. Answer the remaining questions in the lab with these two points removed.
7. Re-do question 6 to see how the correlations change after removing those two data points.
Linear Relationships
8. Select Analyses > Exploration > scatr > Scatterplot, move bty_avg to the X-Axis box, move score to the Y-Axis box, and select Linear under “Regression Line.” Briefly describe how the correlation between score and bty_avg from question 7 summarizes this line.
Analyses > Exploration > scatr > Scatterplot, move age to the X-Axis box, move score to the Y-Axis box, and select Linear under “Regression Line.” Briefly describe how the correlation between score and age from question 7 summarizes this line.bty_avg or age, to predict score, which would produce more accurate predictions on average?References
OpenIntro. (n.d.-a). Data sets [Data sets]. https://openintro.org/data/
OpenIntro. (n.d.-b) CC BY-SA 4.0. Multiple linear regression. OpenIntro Labs for jamovi. https://openintrostat.github.io/oilabs-jamovi/09_multiple_regression/multiple_regression.html
