NPTEL Introduction to Econometrics : Assignment 3

The main purpose of regression analysis is

 To explain the variation in the dependent variable with the variation in independent variables

 To explain the variation in the predicted dependent variable

 To explain the variation in the independent variables with the help of variation in dependent variable

 To explain the variation in the error term

 All of the above

1 point

Degrees of freedom is defined as,

 Number of observations – error terms

 Number of explanatory variables – Number of linear restrictions.

 Number of observations – Number of linear restrictions imposed

 Number of observations – Number of explanatory variables.

 Number of Linear restrictions – Number of observations.

Use the data file “income wealth” to perform a regression analysis in STATA where consumption depends on income. Based on the results obtained answer questions 2-5.

1 point

The value of the intercept (α^$\widehat{�}$) is

 24.54

 -24.54

 24.45

 -24.45

 24.35

1 point

The value of the intercept (β^$\widehat{�}$) is

 0.601

 0.509

 -0.509

 -0.601

 0.519

1 point

How much is the variation in the dependent variable explained by the independent variable in the above model?

 50%

 60%

 51%

 24%

 96%

Given below is the ANOVA results for a two variable regression model for a sample of 10 observations.

1 point

The value of residual sum of squares is

 337.2727

 337.2827

 338.2772

 338.2727

 337.2772

1 point

Degrees of freedom of the Model, residual and total is given respectively as

 (9,1,8)

 (1,9,8)

 (8,9,1)

 (9,8,1)

 (1,8,9)

1 point

MSS of the model is

 8552.7272

 8552.700

 1069.0909

 950.303

 855.2727

1 point

MSS of the source of variation due to RSS is

 33.7272

 337.2727

 42.1590

 37.4747

 339.2727

1 point

F-statistics of the model is equal to

 201.87

 202.87

 203.90

 202.78

 201.78

1 point

The t-statistic is given by

t=(β0–––−β^)/S.E(β^)$�=(\underset{\_}{{�}_0}-\widehat{�})/�.�(\widehat{�})$

t=(β0–––−β^)/S.E(β0)$�=(\underset{\_}{{�}_0}-\widehat{�})/�.�({�}_0)$

t=(β^––−β0)/S.E(β^)$�=(\underset{\_}{\widehat{�}}-{�}_0)/�.�(\widehat{�})$

t=(β^––−β0)/S.E(β0)$�=(\underset{\_}{\widehat{�}}-{�}_0)/�.�({�}_0)$

t=(β^––−β0)∗S.E(β^)$�=(\underset{\_}{\widehat{�}}-{�}_0)\ast �.�(\widehat{�})$

1 point

Accepting a false hypothesis results in

 Type I error

 Type II error

 Structural error

 Hypothesis error

 Both B and C

1 point

Which of the following is/are correct statement in the context of hypothesis testing?

 The power of a test increases as the Type II error probability does

 It is not possible to decrease both Type I and Type II error at the same time

 The significance level is always equal to the probability of Type II error

 A test is significant if it fails to reject the null hypothesis

 All the above

1 point

The value of the test statistic helps deciding

 The number of degrees of freedom of the model.

 The type II error

 Whether to reject or do not reject the null hypothesis.

 Whether to reject or do not reject the alternative hypothesis.

 The value of Critical Region.

1 point

Higher is the difference between the estimated value of the population parameter and the hypothesized value of the population parameter,

 Larger will be the value of test statistic.

 Larger will be the value of degrees of freedom.

 Larger will be the value of Critical region.

 Larger will be the value of intercept coefficient.

 None of the above.

1 point

The size of the critical region is also known as,

 Level of rejection.

 Level of significance.

 Probability of committing Type-I error.

 Confidence interval

 Both B and C.