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Chapter 3: Q 72. (page 209)

Each year, students in an elementary school take a standardized math test at the end of the school year. For a class of fourth-graders, the average score was 55.1 with a standard deviation of 12.3. In the third grade, these same students had an average score of 61.7 with a standard deviation of 14.0. The correlation between the two sets of scores is r = 0.95. Calculate the equation of the least-squares regression line for predicting a fourth-grade score from a third-grade score.

a. y^=3.58+0.835x

b. y^=15.69+0.835x

c. y^=2.19+1.08x

d. y^=−11.54+1.08x

Short Answer

Expert verified

The correct option is (a)y⏜=3.58+0.835x

Step by step solution

01

Given information

y⏜=55.1,sy=12.3,x=61.7,sx=14,r=0.95

02

Explanation

The slope could be calculated as:

b=r×sysx=0.95(12.314.0)=0.835

The intercept could be calculated as:

a=y−bx=55.1−0.835(61.7)=3.60

Thus, the equation of the regression line is:

y⏜=a+bx=3.60+0.835x

Hence, the correct option is (a).

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