# Category: Statistics

## MCQs Econometrics Quiz 5

This quiz is about Econometrics, which covers the topics of Regression analysis, correlation, dummy variable, multicollinearity, heteroscedasticity, autocorrelation, and many other topics. Let’s start with MCQs Econometrics test

MCQs about Econometrics for the preparation of Statistics and Econometrics related Examination and for the PPSC& FPSC and University job related to Lecturer in Statistics, and Statistical Officers.

1. The range of covariance between two variables is:

2. The high value of VIF indicates

3. The range of partial correlation coefficient is:

4. If we have a categorical variable with 4 categories, then how many dummy variables can be used in with intercept regression model

5. Generally, an acceptable value of variance inflation factor (VIF) is:

6. The variance of regression slopes becomes infinite in the case of:

7. Which one is NOT the rule of thumb?

8. If covariance between two variables is positive then their correlation coefficient will always be:

9. The dummy variable trap is basically caused by:

10. Which of these tests is suitable for only a simple regression model.

11. he term Homoscedasticity means

12. Heteroscedasticity refers to situation in which:

13. The dummy variable trap can be avoided by:

14. Variance inflation factor is a common measure for:

15. A variable showing presence or absence of something is known as:

16. In the case of homoscedasticity, we have:

17. When measurement errors are present in the explanatory variable(s) then parameter estimates become

18. In a regression model with 3 explanatory variables, there will be ________ auxiliary regressions

19. In a multiple regression model, the ideal situation is:

20. Eigenvalues can be used for detecting violations of the assumption of:

An application of different statistical methods applied to the economic data used to find empirical relationships between economic data is called Econometrics.

Econometrics means “Economic Measurement”. Econometrics is the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of statistical inference.

Econometrics can also be defined as the empirical determination of economic laws. Econometrics can be classified as (i) Theoretical Econometrics and (ii) Applied Econometrics.

### (i) Theoretical Econometrics

Theoretical econometrics is concerned with developing appropriate methods for measuring economic relationships specified by econometric models. Theoretical econometrics leans heavily on mathematical statistics and must spell out the assumptions of methods (such as Least Squares), their properties, and what happens to these properties when one or more of the assumptions of the technique are not fulfilled.

### (ii) Applied Econometrics

In applied econometrics, the tools of theoretical econometrics are used to study special fields(s) such as production function, investment function, demand and supply function, portfolio theory, etc.

## Types of Econometrics Data

Different type of data is used in Econometrics. There are three important types of data for empirical analysis:

• Time Series Data
A time series data is a set of observations on the values that a variable takes at different times. The time series data may be collected at regular time intervals such as daily, weekly, monthly, quarterly, annually, etc.
• Cross-Sectional Data
Cross-sectional data are data on one or more variables collected at the same point in time. Cross-sectional data has a problem of heterogeneity.
• Pooled Data
Pooled data is a combination of both time series and cross-sectional data.

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## MCQs Econometrics-4

This quiz is about Econometrics, which covers the topics of Regression analysis, correlation, dummy variable, multicollinearity, heteroscedasticity, autocorrelation, and many other topics. Let start with MCQs Econometric test

Please go to MCQs Econometrics-4 to view the test

Try another Econometrics Quiz

## MCQs Econometrics 3

This quiz is about Econometrics, which covers the topics of Regression analysis, correlation, dummy variable, multicollinearity, heteroscedasticity, autocorrelation, and many other topics. Let’s start with MCQs Econometrics test

Please go to MCQs Econometrics 3 to view the test

An application of different statistical methods applied to the economic data used to find empirical relationships between economic data is called Econometrics.

Econometrics means “Economic Measurement”. Econometrics is the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of statistical inference.

Econometrics can also be defined as the empirical determination of economic laws. Econometrics can be classified as (i) Theoretical Econometrics and (ii) Applied Econometrics.

### (i) Theoretical Econometrics

Theoretical econometrics is concerned with developing appropriate methods for measuring economic relationships specified by econometric models. Theoretical econometrics leans heavily on mathematical statistics and must spell out the assumptions of methods (such as Least Squares), their properties, and what happens to these properties when one or more of the assumptions of the technique are not fulfilled.

### (ii) Applied Econometrics

In applied econometrics, the tools of theoretical econometrics are used to study special fields(s) such as production function, investment function, demand and supply function, portfolio theory, etc.

## Types of Econometrics Data

Different type of data is used in Econometrics. There are three important types of data for empirical analysis:

• Time Series Data
A time series data is a set of observations on the values that a variable takes at different times. The time series data may be collected at regular time intervals such as daily, weekly, monthly, quarterly, annually, etc.
• Cross-Sectional Data
Cross-sectional data are data on one or more variables collected at the same point in time. Cross-sectional data has a problem of heterogeneity.
• Pooled Data
Pooled data is a combination of both time series and cross-sectional data.

Try another MCQs Econometrics Quiz

Try a Quiz about Computational Thinking

## MCQs Econometrics-2

This quiz is about Econometrics, which covers the topics of Regression analysis, correlation, dummy variable, multicollinearity, heteroscedasticity, autocorrelation, and many other topics. Let’s start with MCQs Econometrics test

Please go to MCQs Econometrics-2 to view the test

An application of different statistical methods applied to the economic data used to find empirical relationships between economic data is called Econometrics.

Econometrics means “Economic Measurement”. Econometrics is the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of statistical inference.

Econometrics can also be defined as the empirical determination of economic laws. Econometrics can be classified as (i) Theoretical Econometrics and (ii) Applied Econometrics.

### (i) Theoretical Econometrics

Theoretical econometrics is concerned with developing appropriate methods for measuring economic relationships specified by econometric models. Theoretical econometrics leans heavily on mathematical statistics and must spell out the assumptions of methods (such as Least Squares), their properties, and what happens to these properties when one or more of the assumptions of the technique are not fulfilled.

### (ii) Applied Econometrics

In applied econometrics, the tools of theoretical econometrics are used to study special fields(s) such as production function, investment function, demand and supply function, portfolio theory, etc.

## Types of Econometrics Data

Different type of data is used in Econometrics. There are three important types of data for empirical analysis:

• Time Series Data
A time series data is a set of observations on the values that a variable takes at different times. The time series data may be collected at regular time intervals such as daily, weekly, monthly, quarterly, annually, etc.
• Cross-Sectional Data
Cross-sectional data are data on one or more variables collected at the same point in time. Cross-sectional data has a problem of heterogeneity.
• Pooled Data
Pooled data is a combination of both time series and cross-sectional data.

Try another MCQs Econometrics Quiz

Try a Quiz about Computational Thinking

## Chi-Square Test of Independence

Chi-square test is a non-parametric test. The assumption of normal distribution in the population is not required for this test. The statistical technique chi-square can be used to find the association (dependencies) between sets of two or more categorical variables by comparing how close the observed frequencies are to the expected frequencies. In other words, a chi square ($\chi^2$) statistic is used to investigate whether the distributions of categorical variables different from one another. Note that the response of categorical variables should be independent from each other. We use the chi-square test for relationship between two nominal scaled variables.

Chi-square test of independence is used as tests of goodness of fit and as tests of independence. In test of goodness of fit, we check whether or not observed frequency distribution is different from the theoretical distribution, while in test of independence we assess, whether paired observations on two variables are independent from each other (from contingency table).

Example: A social scientist sampled 140 people and classified them according to income level and whether or not they played a state lottery in the last month. The sample information is reported below. Is it reasonable to conclude that playing the lottery is related to income level? Use the 0.05 significance level.

 Income Low Middle High Total Played 46 28 21 95 Did not play 14 12 19 45 Total 60 40 40 140

Step by step procedure of testing of hypothesis about association between these two variable is described, below.

Step1:
$H_0$: There is no relationship between income and whether the person played the lottery.
$H_1$: There is relationship between income and whether the person played the lottery.

Step2: Level of Significance 0.05

Step 3: Test statistics (calculations)

 Observed Frequencies ($f_o$$f_o$) Expected Frequencies ($f_e$$f_e$) $\frac{(f_o - f_e)^2}{f_e}$$\frac{(f_o - f_e)^2}{f_e}$ 46 95*60/140= 40.71 $\frac{(46-40.71)^2}{40.71}$$\frac{(46-40.71)^2}{40.71}$ 28 95*40/140= 27.14 $\frac{(28-27.14)^2}{27.14}$$\frac{(28-27.14)^2}{27.14}$ 21 95*40/140= 27.14 $\frac{(21-27.14)^2}{27.14}$$\frac{(21-27.14)^2}{27.14}$ 14 45*60/140= 19.29 $\frac{(14-19.29)^2}{19.29}$$\frac{(14-19.29)^2}{19.29}$ 12 45*40/140= 12.86 $\frac{(12-12.6)^2}{12.86}$$\frac{(12-12.6)^2}{12.86}$ 19 45*40/140= 12.86 $\frac{(19-12.86)^2}{12.86}$$\frac{(19-12.86)^2}{12.86}$ $\chi^2=\sum[\frac{(f_0-f_e)^2}{f_e}]=$$\chi^2=\sum[\frac{(f_0-f_e)^2}{f_e}]=$ 6.544

Step 4: Critical Region:
Tabular Chi-Square value at 0.05 level of significance and $(r-1) \times (c-1)=(2-1)\times(3-1)=2$ is 5.991.

Step 5: Decision
As calculated Chi-Square value is greater than tabular Chi-Square value, we reject $H_0$, which means that there is relationship between income level and playing the lottery.

Note that there are several types of chi-square test (such as Yates, Likelihood ratio, Portmanteau test in time series) available which depends on the way data was collected and also the hypothesis being tested.