Suppose the institute who conduct SAT examination would like to examine the relationship

between SAT score obtained by a candidate (Y =score out of 1600) and previous school level math score(X1= marks out of 100) and English score X2= marks out of 100). The data on 35 candidates on these variables were obtained. The least squares estimate are given below:

Y = 1220 + 1.3X₁ + 0.8X₂

with SE( B^ ₁) = Sb₁ = 0.174; SE( B^ ₂) = Sb₂ = 0.141 and SST=12036, SSE=3050

[NOTE: B^= beta]

(a) Interpret the estimate of the each of the coeficient. [3]

(b) What percentage of variation in SAT score can be explained by the school level math

score?

(c) Test at 2.5% level of significance whether there is any positive association of English

score on SAT score

(d) Find the predicted SAT score for a new students who scored 85 in MATH and 73 in English.