Question

Given are the data for two variables, X and y. Do not round your intermediate calculations.

xi 6 11 15 18 20
yi 6 8 12 20 30

Develop an estimated regression equation for these data by computing bị and bo (to 3 decimals). Enter negative values as negative numbers.
bi=_____

Answer 1

The estimated regression equation is ŷ = 1.5873X - 7.02222.

The mean of X and y:

Mean of X (mean_x) = (6 + 11 + 15 + 18 + 20) / 5 = 14

Mean of y (mean_y) = (6 + 8 + 12 + 20 + 30) / 5 = 15.2

Calculate the sum of squared deviations from the mean for X and y:

Sum of squared deviations from the mean for X (SS_X) = (6-14)² + (11-14)² + ... + (20-14)² = 92

Sum of squared deviations from the mean for y (SS_y) = (6-15.2)² + (8-15.2)² + ... + (30-15.2)² = 254.8

Calculate the covariance between X and y:

Covariance (cov_xy) = Σ[(xi - mean_x)(yi - mean_y)] = (6-14)(6-15.2) + ... + (20-14)(30-15.2) = 145.6

Calculate the slope (b1):

b1 = cov_xy / SS_X = 145.6 / 92 = 1.5873 (rounded to 3 decimals)

Calculate the intercept (b0):

b0 = mean_y - b1 * mean_x = 15.2 - 1.5873 * 14 = -7.02222 (rounded to 3 decimals)

Therefore, the estimated regression equation is ŷ = 1.5873X - 7.02222.