When estimating yˆ = β0 + β1×1 + β2×2 + ε, the following regression results using ANOVA were obtained. df SS MS F Regress

Question

When estimating yˆ = β0 + β1×1 + β2×2 + ε, the following regression results using ANOVA were obtained.

df SS MS F
Regression 2 210.9 105.5 114.7
Residual 17 15.6 0.92
Total 19 226.5
Coefficients Standard Error t-stat p-value
Intercept −1.6 0.57 −2.77 0.0132
x1 −0.5 0.04 −15.11 2.77E-11
x2 0.1 0.07 1.89 0.0753

Which of the following is the adjusted R2?

A. 0.92
B. 0.82
C. 0.96
D. 0.86

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Bella 6 days 2021-09-13T13:04:23+00:00 1 Answer 0

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    2021-09-13T13:05:23+00:00

    Answer:

    A) The adjusted  R²  = 0.923

    Step-by-step explanation:

    Given data

    sum of squares of regression (SSR) = 210.9

    Sum of squares of residuals = 15.6

    Total sum of squares(SST) = 226.5

    Degrees of freedom of Regression = 2

    Degrees of freedom of Residuals = 17

    Total number of degrees of freedom = 19

    The R² is determined by

    R^{2} = \frac{Regression SS}{Total SS}

    R^{2} = \frac{210.9}{226.5} = 0.9311

    Adjusted R² is determined by

    R⁻²    = 1-(1-R^{2})(\frac{n-1}{n-k-1)})

    The degrees of  freedom of residuals  

    n -k-1  = 17

    given data k= 2 (degrees of freedom of regression = 2)

    n – 2 -1 =17

    n = 17 +3 =20

    The Adjusted  R²

                                    = 1-(1-R^{2})(\frac{n-1}{n-k-1)})

                                    = 1-(1-0.9311)(\frac{20-1}{17})

    on calculation, we get

    R⁻²    = 0.923

    Final answer:-

    The adjusted  R²  = 0.923

                 

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