Question

The National Assessment for Educational Progress (NAEP) is a U.S. government organization that assesses the performance of students and schools at all levels across the United States. The following table presents the percentage of eighth-grade students who were found to be proficient in mathematics, and the percentage who were found to be proficient in reading in each of the ten most populous states.

State	Percentage proficient in Reading	Percentage proficient in Mathematics
California	60	59
Texas	73	78
New York	75	70
Florida	66	68
Illinois	75	70
Pennsylvania	79	77
Ohio	79	76
Michigan	73	66
Georgia	67	64
North Carolina	71	73

a. Identify the explanatory variable (x) and the response variable (y).

Explanatory variable:

Response variable

b. Use your calculator to find the correlation coefficient ?. Based on the correlation coefficient, what can you say about the association between proficiency in reading and proficiency math?

? =

c. State the least squares regression line ?̂. (Use your calculator)

d. Within the context of the problem give an interpretation of the intercept of ?̂.

e. Find the best predicted percentage proficiency in Math for a student who has a proficiency of 70 percent in Reading.

Answer 1

a)

Explanatory variable:   Percentage proficient in Reading

Response variable : Percentage proficient in Mathematics

b) Correlation Coefficient:

c) Regression equation:

d) Slope = 0.8226 which is >0 therefore there is positive correlation between percentage proficiency in Math and Percentage proficient in Reading

i.e. As Percentage proficient in Reading increases 1 unit of time, percentage proficiency in Math is also increased by 0.8226.

Intercept: 11.0358

If Percentage proficient in Reading is zero then percentage proficiency in Math will be 11.0358

but this interpretation is meaningless since Zero is not in Percentage proficient in Reading variable of the data

e) The best predicted percentage proficiency in Math for a student who has a proficiency of 70 percent in Reading is