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.
c. does there appear to be a linear association between the high school gpa and the college gpa? explain your reasoning.
(table and scatterplot image description: table has columns student, high school gpa, college gpa with 12 rows of data. scatterplot has x-axis high school gpa, y-axis college gpa with some plotted points.)

Explanation:

Part (a)

Step1: Define Explanatory Variable

The explanatory variable is the one that is used to explain or predict changes in another variable. Here, high school GPA is thought to influence college GPA, so it's the explanatory variable.

Step2: Define Response Variable

The response variable is the one that is being measured or predicted. College GPA is the outcome we're interested in, so it's the response variable.

Step1: Identify Coordinates

For each student, the x - coordinate is the High School GPA and the y - coordinate is the College GPA. For example, Student 1: (2.22, 2.35), Student 2: (2.50, 2.80), Student 3: (3.42, 3.88), Student 4: (3.45, 3.40), Student 5: (2.45, 2.95), Student 6: (2.67, 3.1), Student 7: (3.24, 3), Student 8: (3.80, ), Student 9: (3.11, ), Student 10: (3.15, ), Student 11: (3.25, ), Student 12: (2.88, ).

Step2: Plot Points

On the scatterplot with x - axis as High School GPA and y - axis as College GPA, plot each of these points. For the points with missing College GPA (Students 8 - 11), we assume the data is complete as per the problem's context (maybe a typo in the image), but for the given data, we plot the available coordinates.

Step1: Analyze Trend

When we look at the general pattern of the points (even with some missing values), as the high school GPA (x - value) increases, the college GPA (y - value) also tends to increase.

Step2: Check Linearity

The points seem to follow a roughly straight - line pattern. There is a positive association, and the pattern of the points is consistent with a linear relationship (the points cluster around a potential straight line).

Answer:

Explanatory variable: High School GPA
Response variable: College GPA

Part (b)