SAT Prep Case Study

Introduction:

As every student in the USA Europe and Australia knows, you have to pass the SAT or IB to get accepted into University—which over the years has become more and more challenging. Today it is not enough to just pass the exam but you have to be average or above the average in order to even be considered for university or College. Therefore many students decide to go too an SAT prep school such as Princeton or to a higher education facility. As many of us also know Colleges Universities and Prep Schools are quite expensive so for some middle and lower class societies it is considered to be luxury to attend either one. So one might say that these kind of institutions are more available for the upper classes and could be considered

Scatter Plot of above Data:

The below graph seems to show that there is some corrolation between test scores and family income. Least Square Regression

Leas square regression:

The Least Square regression identifies the relationship between the independent variable, x, and the dependent variable, y. It is given by the following formula: y-y ̅= S_xy/S_(x^2 ) (x-x ̅) where S_xy= (∑▒xy)/n- x ̅y ̅ and S_(x^2 )=√((∑▒x^2 )/n-(x^2 ) ̅ ) m(slope)=nxy-(x)(y)nx2-(x)2 b(y intercept)= y-m(x)n

Y=mx+b

Table 2: Values of Least Squares Regression x y xy x2

15000 1301 19515000 225000000

25000 1371 34275000 625000000

35000 1363 47705000 1225000000

45000 1427 64215000 2025000000

55000 1462 80410000 3025000000

65000 1487 96655000 4225000000

75000 1508 113100000 5625000000

85000 1522 129370000 7225000000

95000 1559 148105000