Statistical software was used to fit the model E(y) = beta_0 + beta_1 x_1 + beta

Question

Statistical software was used to fit the model E(y) = beta_0 + beta_1 x_1 + beta_2 x_2 to n = 20 f. Find R^2 and R^2_a and interpret these values. R^2 = 5.1% indicates the percentage of the total sample variation of the y-value sample size and the number of beta parameters in the model. (Type integers or decimals) g. Find the test statistic for testing H_0: beta_1 = beta_2 = 0. The test statistic is 8.78. (Type an integer or a decimal) h. Find the observed significance level of the test in part g. Interpret the result. The observed significance level is .002 (Type an integer or a decimal) Interpret this value. The observed significance level indicates that of the coefficients can be considered useful for predicting y at that level The regression equation is Y = 3606.89 - 2562.94x_1 - 290 95x_2

Explanation / Answer

f)

R^2 = 51 %

R2a = 45    %       {see the line in between two tables}

g)

F = (r^2/k) / ((1-r^2)/(n-k-1))

= (0.51/2)/((1-0.51)/17)

= 8.846938

h) p-value = P(F > 8.846938) = 0.002

with df1 = 2 , df2 = 17

f) since p-value =   0.05

we reject the null and conclude that

both coefficients are jointly significant

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