Question

1. ms. tanaka is a guidance counselor at a local high school. she is giving a presentation to the freshman class about the importance of studying and getting good grades. she displays data she collected on 12 previous students and their progress in college. the data includes the students’ high school gpa and their first year college gpa. the table shows the data she has collected.

a. identify the explanatory and response variables.
b. graph the data to complete the scatterplot.
(table and scatterplot grid as shown in the image)

Explanation:

Part (a)

Step1: Recall Variable Definitions

Explanatory variable (independent) is what we think causes change, response (dependent) is the outcome.

Step2: Analyze the Context

High school GPA is used to explain college GPA. So:

• Explanatory: High school GPA (variable explaining change)
• Response: First - year college GPA (variable responding to change)

Step1: Understand Scatterplot Axes

x - axis: High School GPA (ranges 2.2 - 3.8), y - axis: College GPA (ranges ~2.2 - 3.8).

Step2: Plot Each Data Point

For each student:

• Student 1: (2.22,? ) [need college GPA, but assume table has it, plot (2.22, college GPA1)]
• Student 2: (2.50, college GPA2)
• Student 3: (3.42, college GPA3)
• Student 4: (3.45, college GPA4)
• Student 5: (2.45, college GPA5)
• Student 6: (2.67, college GPA6)
• Student 7: (3.24, college GPA7)
• Student 8: (3.80, college GPA8) (and others if table has more). Locate x (high school GPA) on x - axis, y (college GPA) on y - axis, mark the point.

(Note: Since full table of college GPAs isn't visible, but the process is to plot each (high school GPA, college GPA) pair on the given grid.)

Answer:

Explanatory variable: High school GPA
Response variable: First - year college GPA

Part (b)