n i=1 - - let denote the sample correlation coefficient between Y and X (defined...

 

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n i=1 - - let ô denote the sample correlation coefficient between Y and X (defined formally below), and let ô² = 1½ Σ₁(yi — ÿ)² and ô² = ½-½ Σ²±1(xi−)². (These notations are also defined in slides 44-46 of Chapter 1 Part A notes.) Then, prove that ẞ₁ from above also satisfies the following form: ẞ1 = X ÔY ρ where = n ox - (xi)(yi — ÿ) - n √√Σ²Î²±1(xi — ñ)² √√Σ² ²±1 (Yi — ÿ)² σχ ông = với and ôx = với 1 and with as above. What does this result tell us about the nature of the relationship between B₁ and p? And also between B² and p² (which is the same as R², the coefficient of determination)? (Note: For all proofs above, you must show in detail all your steps in arriving at the final conclusions.) n i=1 - - let ô denote the sample correlation coefficient between Y and X (defined formally below), and let ô² = 1½ Σ₁(yi — ÿ)² and ô² = ½-½ Σ²±1(xi−)². (These notations are also defined in slides 44-46 of Chapter 1 Part A notes.) Then, prove that ẞ₁ from above also satisfies the following form: ẞ1 = X ÔY ρ where = n ox - (xi)(yi — ÿ) - n √√Σ²Î²±1(xi — ñ)² √√Σ² ²±1 (Yi — ÿ)² σχ ông = với and ôx = với 1 and with as above. What does this result tell us about the nature of the relationship between B₁ and p? And also between B² and p² (which is the same as R², the coefficient of determination)? (Note: For all proofs above, you must show in detail all your steps in arriving at the final conclusions.)