Question

The regression model Yi = ?? + ??X?i + ??X?i + ui has been estimated using Gretl. The output is below. Model 1: OLS, using observations 1-53 coefficient std. error t-ratio p-value const -0.5427 0.1341 -4.0484 0.0002 X1 0.7071 0.0731 9.6684 0.0000 X2 -0.7121 0.0802 -8.8832 0.0000 Mean dependent var 0.8828 S.D. dependent var 1.4945 Sum squared resid 20.492 S.E. of regression 0.64019 R-squared 0 Adjusted R-squared -0.04 F(2, 50) 116.7 P-value(F) 0 Log-likelihood -50.022 Akaike criterion 106.04 Schwarz criterion 111.95 Hannan-Quinn 108.32 a. (7 marks) Construct the ANOVA table for this estimated model. Your answer should include a table consisting of columns for the sum of squares, degrees of freedom, and mean square, and rows labelled 'Estimated', 'Residual' and 'Total'. In addition to providing the completed table, you should provide an explanation of how you computed each element. b. (3 marks) Notice that the R² has been set to 0, which is clearly incorrect. Calculate the correct R² for this estimated model. Show your working.

          The regression model

Yi = ?? + ??X?i + ??X?i + ui

has been estimated using Gretl. The output is below.

Model 1: OLS, using observations 1-53
             coefficient    std. error    t-ratio    p-value
const        -0.5427        0.1341        -4.0484    0.0002
X1            0.7071        0.0731         9.6684    0.0000
X2           -0.7121        0.0802        -8.8832    0.0000
Mean dependent var      0.8828   S.D. dependent var      1.4945
Sum squared resid       20.492   S.E. of regression       0.64019
R-squared               0        Adjusted R-squared     -0.04
F(2, 50)                116.7    P-value(F)              0
Log-likelihood         -50.022   Akaike criterion        106.04
Schwarz criterion       111.95   Hannan-Quinn            108.32

a. (7 marks) Construct the ANOVA table for this estimated model. Your answer should include a table consisting of columns for the sum of squares, degrees of freedom, and mean square, and rows labelled 'Estimated', 'Residual' and 'Total'. In addition to providing the completed table, you should provide an explanation of how you computed each element.

b. (3 marks) Notice that the R² has been set to 0, which is clearly incorrect. Calculate the correct R² for this estimated model. Show your working.

Show more…

The regression model

Yi = ?? + ??X?i + ??X?i + ui

has been estimated using Gretl. The output is below.

Model 1: OLS, using observations 1-53
coefficient std. error t-ratio p-value
const -0.5427 0.1341 -4.0484 0.0002
X1 0.7071 0.0731 9.6684 0.0000
X2 -0.7121 0.0802 -8.8832 0.0000
Mean dependent var 0.8828 S.D. dependent var 1.4945
Sum squared resid 20.492 S.E. of regression 0.64019
R-squared 0 Adjusted R-squared -0.04
F(2, 50) 116.7 P-value(F) 0
Log-likelihood -50.022 Akaike criterion 106.04
Schwarz criterion 111.95 Hannan-Quinn 108.32

a. (7 marks) Construct the ANOVA table for this estimated model. Your answer should include a table consisting of columns for the sum of squares, degrees of freedom, and mean square, and rows labelled 'Estimated', 'Residual' and 'Total'. In addition to providing the completed table, you should provide an explanation of how you computed each element.

b. (3 marks) Notice that the R² has been set to 0, which is clearly incorrect. Calculate the correct R² for this estimated model. Show your working.

Added by Vanessa P.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

06/19/2023

Step 1

238 | 2 | 11.619 | 116.7 | 0.0000 Residual | 20.492 | 50 | 0.410 | - | - Total | 43.730 | 52 | - | - | - To compute the ANOVA table, we need to calculate the sum of squares (SS), degrees of freedom (df), and mean square (MS) for each source of variation. - Show more…

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The regression model Yi = β0 + β1X1i + β2X2i + ui has been estimated using Gretl. The output is below. Model 1: OLS, using observations 1-53 coefficient std. error t-ratio p-value const -0.5427 0.1341 -4.0484 0.0002 X1 0.7071 0.0731 9.6684 0.0000 X2 -0.7121 0.0802 -8.8832 0.0000 Mean dependent var 0.8828 S.D. dependent var 1.4945 Sum squared resid 20.492 S.E. of regression 0.64019 R-squared 0 Adjusted R-squared -0.04 F(2, 50) 116.7 P-value(F) 0 Log-likelihood -50.022 Akaike criterion 106.04 Schwarz criterion 111.95 Hannan-Quinn 108.32 a. (7 marks) Construct the ANOVA table for this estimated model. Your answer should include a table consisting of columns for the sum of squares, degrees of freedom, and mean square, and rows labelled 'Estimated', 'Residual' and 'Total'. In addition to providing the completed table, you should provide an explanation of how you computed each element. b. (3 marks) Notice that the R² has been set to 0, which is clearly incorrect. Calculate the correct R² for this estimated model. Show your working.

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Transcript

00:01 So, here it is given a regression model yi is equal to beta naught plus beta 1 of x1i plus beta 2 of x2i plus u of i which has been estimated using ratio.

00:23 So the output is given below.

00:25 So we have to construct anova table to estimate the model.

00:30 So let's suppose the regression output can be given by x1 and x2.

00:38 So let's say x1 and x2 are independent variables and let's say y is dependent variable.

00:50 So according to this, the degree of freedom which is denoted by df for the regression, this would become equals to how much? that is 2 because we are having the two independent variables while degree of freedom in regards to the error that having to be occurring which should be equals to 50 and hence the degree of freedom for the total would becomes 2 plus 50 that is 52 and hence we can clearly say that the sample space or sample size that is n which indicate the total observations was to 53 which we have been given into the table.

01:32 So from here the ss residual this would become equals to 20 .492 from the given output and ms residual would become equals to this is residual that divided by the degree of freedom of residual so that will be equals to 20 .492 by the total degree of freedom that is 53.

02:04 So will comes out 0 .3866.

02:08 So ms regression this would become equals to the statistics into the ms residual.

02:17 So statistics is 116 .7 multiplied by the ms residual we have just found 0 .3866.

02:26 So would comes out equals to 45 .11622.

02:31 So this is what the ms regression.

02:34 Now the next thing that we need to find before the table to be constructed that is the ss regression.

02:42 So that will be equals to the ms regression times the degree of freedom degree of freedom regression.

02:51 So this should be equals to 45 .11622 times of 2 would comes out 90 .23244...

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