Let Yi=v¯¯¯(v¯¯¯TXi) , or equivalently v¯¯¯(v¯¯¯⋅Xi)=(v¯¯¯⋅Xi)v¯¯¯ , where v¯¯¯=v∥v∥ is the same as in part (c). We will compare the asymptotic distribution of X¯¯¯¯n you obtain in part (d) to the asymptotic distribution of Y¯¯¯¯n where Y¯¯¯¯n=∑niYin . What is the expectation E[Yi] of Yi ?

Step-by-step explanation:

A mathematics teacher wanted to see the correlation between test scores and homework. The homework grade (x) and test grade (y) are given in the accompanying table. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, estimate the homework grade, to the nearest integer, for a student with a test grade of 31.

Homework Grade (x) Test Grade (y)

58 52

75 66

66 68

85 74

52 38

74 65

78 76