Eachyearstudentsinanelementaryschooltakea standardized math

Eachyear,studentsinanelementaryschooltakea 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 equa- tion of the least-squares regression line for predicting a fourth-grade score from a third-grade score.

(a)y^= 3.60 + 0.835x (b)y^ = 15.69 + 0.835x (c)y^ = 2.19 + 1.08x
(d) y^ = 11.54 + 1.08x (e) Cannot be calculated
without the dat

Solution

The regression equation can be written as:

Y^=b+ax^

Now, a=r*sy/sx=0.95*12.3/14=0.835

b=y bar- a *x bar=55.1-0.835*61.7=3.5805

Thus, the required regression equation is:

Y^=3.5805+0.835 x^