Question

You are conducting a study to determine if there is a relationship between annual household income and a high school student’s GPA. The school district you are studying is diverse and lower income.

a) Before you conduct the study, do you expect there to be an association between these two variables? Why or why not? Which should be the explanatory variable?

b) You collect data from a random sample of 15 students. The first row of the table is household income of a particular student (in thousands of dollars) and the second row is the GPA of that particular student.

42	30	82	19	29	44	90	55	17	62	51	30	9	39	42
3.1	2.6	3.8	2.7	2.3	3.5	3.8	3.2	2.4	3.3	3.1	2.8	1.6	3.4	3.2

c) Does the data have a scatterplot that shows a linear association? What is the correlation coefficient? What does it tell you about the association between these two variables?

d) Use the above data to make a linear (regression) model.

e) Use the model to predict the GPA of a high-schooler that comes from a family that has a household income of $48,000.

f) How accurate is the model’s prediction of GPA for the family that makes $44,000?

g) If a family’s income increases by $10,000, what is the amount of change in a student’s GPA, as predicted by the model?

h) Statisticians often state “correlation is not necessarily causation.” Would it be correct to conclude that household income is “causing” GPA? Is it possible that there are other variables that are “lurking,” causing GPA and household income to be correlated? What might these variables be?

Answer 1

Dear student, we can answer only four subparts at a time, please help to upload other parts separately.

a)

According to me, the association between annual household income and a high school student GPA will not be that strong but there are some factors that make these variables associated.

High the salary is, more are the facilities to the student and with more facilities, there can be an impact on GPA. More income will lead to more GPAs according to me.

b)

Income	GPA
42	3.1
30	2.6
82	3.8
19	2.7
29	2.3
44	3.5
90	3.8
55	2.2
17	2.4
62	3.3
51	3.1
30	2.8
9	1.6
39	3.4
42	3.2

c)

The scatterplot comes out to be-

It shows the linear relationship between these two variables.

The correlation comes out to be 0.76173.

d)

The equation comes out to be-

GPA = 2.025 + 0.0209*Income  

e)

When income = 48

GPA = 2.025 + 0.0209*48 = 3.02