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	66	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)The explanatory variable (x) and the response variable (y).

Explanatory variable: Percentage proficient in reading

Response variable: Percentage proficient in mathematics.

State	X	Y	(x-xbar)2	(y-ybar)2	(x-xbar)(y-ybar)
California	60	59	123.21	123.21	123.21
Texas	66	78	26.01	62.41	-40.29
New York	75	70	15.21	0.01	-0.39
Florida	66	68	26.01	4.41	10.71
Illinois	75	70	15.21	0.01	-0.39
Pennsylvania	79	77	62.41	47.61	54.51
Ohio	79	76	62.41	34.81	46.61
Michigan	73	66	3.61	16.81	-7.79
Georgia	67	64	16.81	37.21	25.01
North Carolina	71	73	0.01	8.41	-0.29
Total	711	701	350.9	334.9	210.9
Mean	71.1	70.1

b) The correlation coefficient is given by,

  

r = 0.62

Correlation coefficient = 0.62 indicates moderate positive relationship. Hence, they are not associated.

c) The least square regression line is,

b = 210.9 / 350.9 = 0.60

a = 70.1 - (71.1*0.60) = 27.37

Hence, the regression line is,

d) Here, y intercept = 27.37 , which means if a percentage proficient in reading = 0, then percent profficient in mathemaatics is 27.37

e) Given, percentage proficient in reading = 70,

   the best predicted percentage proficiency in Math is,

  

= 69.37

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