1.
When testing r linear restrictions imposed on the model y = β0 + β1x1 + ... + βkxk + ε, the test statistic is assumed to follow the F(df1, df2) distribution with ____________________.
df1 = k and df2 = n – k – 1
df1 = k – 1 and df2 = n – k – 1
df1 = r and df2 = n – k
df1 = r and df2 = n – k – 1
2.
(Round all intermediate calculations to at least 4 decimal places.) |
Consider the following sample regressions for the linear, the quadratic, and the cubic models along with their respective R2 and adjusted R2. |
Linear | Quadratic | Cubic | |
Intercept | 9.45 | 9.78 | 9.84 |
x | 2.60 | 2.69 | 1.79 |
x2 | NA | −0.30 | −0.32 |
x3 | NA | NA | 0.25 |
R2 | 0.790 | 0.818 | 0.877 |
Adjusted R2 | 0.791 | 0.815 | 0.876 |
a. |
Predict y for x = 2 and 3 with each of the estimated models. (Round your answers to 2 decimal places.) |
Linear yˆy^ | Quadratic yˆy^ | Cubic yˆy^ | |
x = 2 | |||
x = 3 | |||
b. | Select the most appropriate model. | ||||||
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1.
When testing r linear restrictions imposed on the model y = β0 + β1x1 + ... + βkxk + ε, the test statistic is assumed to follow the F(df1, df2) distribution with df1 = r and df2 = n – k – 1
1. When testing r linear restrictions imposed on the model y = β0 + β1x1 + ... + βkxk + ε, the test statistic is assumed to follow the F(df1, df2) distribution with ____________________. df1 = k and d...
1. When testing r linear restrictions imposed on the model y = β0 + β1x1 + ... + βkxk + ε, the test statistic is assumed to follow the F(df1, df2) distribution with ____________________. df1 = k and df2 = n – k – 1 df1 = k – 1 and df2 = n – k – 1 df1 = r and df2 = n – k df1 = r and df2 = n – k – 1 2. (Round...
e. Consider the multiple regression model y X 3+E. with E(e)-0 and var (e) ơ21 Assume that ε ~ N(0 σ21), when we test the hypothesis Ho : βί-0 against Ha : βί 0 we use the t statistic with n-k-1 degrees of freedom. When Ho is not true find the expected value and variance of the test onsider the genera -~ 0 gains 0 1S not true find the expected value and variance of the test statistic. e. Consider...