Regression Lines - See question?

[ADAMT1616]

Hi there can any help me answer the following questions, stats is driving p the wall!!! ThanksMarks (out of 100) on Mathematics and English tests have means 45 and 50, respectively, and one student scores 40 in Mathematics and 60 in English. Given that the regression line for predicting English marks from Mathematics marks (a) passes through the point defined by the means, and (b) predicts this student’s English mark as 70, show thatthe regression line isE = 230 − 4 ×Mwhere E,M denote the English and Mathematics marks respectively. Further show that it is not sensible to use the regression line whenM < 32.5 or M > 57.5.2

[mathsmanretired9848]

The E on M regression line passes through both means so it must beE - 50 = s(M - 45)where s is the the slope.If it predicts 70 as the English mark for mathematics 40 then70 - 50 = s(40 - 45)20 = -5ss = -4which is a weird result !Therefore the regression line isE - 50 = -4(M - 45)E - 50 = -4M + 180E = -4M + 230 or E = 230 - 4MIf M < 32.5 then E > 230 - 4*32.5 = 100 ----> E > 100If M > 57.5 then E < 230 - 4*57.5 = 0 ----> E < 0You may wonder why I have used the opposite sign in each of the last two lines. This is because multiplying by a negative number reverses the sign of an inequality.