Fitting Linear Models to Data: Apply It 1

  • Use linear functions to model and draw conclusions from real-world problems
  • Sketch scatter plots to see patterns and tell apart straight-line relationships from curves
  • Find the best straight line that goes through a set of data points
  • Identify the differences between linear and nonlinear relations
Scatterplots are used to illustrate the relationship between two variables in a data set.Colleagues talking and pointing to a whiteboard with drawings of figures

George, a current student, got a [latex]36[/latex] out of [latex]50[/latex] on the first midterm (C-). He asked his instructor, “If I don’t change my study approach, how do you predict I will do on the final exam?”

One way to answer this question is to look at the bivariate data of student scores from a previous class. In this case, we choose a random sample of past students who did not seek out additional tutoring and/or support between the midterm and the final.

The following is a data set from a random sample of past students who did not seek out advice on study skills or additional tutoring between the midterm and the final exam. To protect their anonymity, only first names are shown.

Student First Name Midterm Score

(out of [latex]50[/latex] points)

 Final Exam Score

(out of [latex]100[/latex] points)
Joe [latex]42[/latex] [latex]64[/latex]
Barak [latex]52[/latex] [latex]94[/latex]
Hillary [latex]44[/latex] [latex]87[/latex]
Donald [latex]25[/latex] [latex]46[/latex]
Cher [latex]41[/latex] [latex]73[/latex]
Katy [latex]39[/latex] [latex]73[/latex]
Taylor [latex]33[/latex] [latex]53[/latex]
Miley [latex]40[/latex] [latex]77[/latex]
Justin [latex]35[/latex] [latex]60[/latex]
Snoop [latex]31[/latex] [latex]62[/latex]
Bruno [latex]37[/latex] [latex]71[/latex]
Kanye [latex]49[/latex] [latex]95[/latex]
Leonardo [latex]38[/latex] [latex]70[/latex]
Rosie [latex]45[/latex] [latex]80[/latex]
Maya [latex]49[/latex] [latex]80[/latex]
Tyra [latex]48[/latex] [latex]82[/latex]
Selena [latex]50[/latex] [latex]81[/latex]
Steps to create the scatterplot and the linear regression line:

Step 1: Under Enter Data, select Enter Own.

Step 2: Name the X (explanatory) and Y (response) variables appropriately.

Step 3: Copy and paste the data set.

Step 4: Under Plot Options, select Regression Line, and click the Submit Data button.

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