The following table shows the age ( X ) and systolic blood pressure ( Y ) of 8 persons. Age ( X ) 56 42 60 50 54 49 39 45 Blood pressure ( Y ) 160 130 125 135 145 115 140 120 Fit a simple linear regression model, Y on X and estimate the blood pressure of a person of 60 years.

Given that, the data of age ( X ) and blood pressure ( Y ) . Age ( X ) Blood pressure ( Y ) X 2 Y 2 X . Y 56 160 3136 25600 8960 42 130 1764 16900 5460 60 125 3600 15625 7500 50 135 2500 18225 6750 54 145 2916 21025 7830 49 115 2401 13225 5635 39 140 1521 19600 5460 45 120 2025 14400 5400 Σ X = 395 Σ Y = 1070 Σ X 2 = 19863 Σ Y 2 = 144600 Σ X Y = 52995 We know that, regression equation of Y on X is Y = a + b Y X X , where b Y X = n ∑ i = 1 n x i y i - ∑ i = 1 n x i × ∑ i = 1 n y i n ∑ i = 1 n x i 2 - ∑ i = 1 n x i 2 and a ^ = 1 n ∑ i = 1 n y i - b ^ 1 n ∑ i = 1 n x i ⇒ b Y X = 8 52995 - 395 × 1070 8 19863 - 395 2 = 0 . 455 ⇒ a = 1070 8 - 0 . 455 8 395 = 111 . 284 ∴ Regression equation of Y on X is Y = 111 . 284 + 0 . 455 X .