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Q35Section ST (Statistics (Q11–Q65))35 of 65

Adjusted R-squared from R-squared

Consider the multi-linear regression model yi=β0+β1x1i+β2x2i+β3x3i+β4x4i+ϵi,  i=1,2,…,25y_i = \beta_0 + \beta_1 x_{1i} + \beta_2 x_{2i} + \beta_3 x_{3i} + \beta_4 x_{4i} + \epsilon_i, \; i = 1, 2, \dots, 25, where βi\beta_i, i=0,1,2,3,4i = 0, 1, 2, 3, 4, are unknown parameters, the errors ϵi\epsilon_i's are i.i.d. random variables having N(0,σ2)N(0, \sigma^2) distribution, where σ>0\sigma > 0 is unknown. Suppose that the value of the coefficient of determination R2R^2 is obtained as 56\frac{5}{6}. Then the value of adjusted R2R^2 is __________ (rounded off to two decimal places).

Numerical answer: type the number (no options).

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