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Econometrics questions.

Econometrics questions.

Find Econometrics university examination questions in acaproso.com

# Question
1

The Chi-square contigency test statistics is widely used in economic analysis

  1. What is the purpose of using such a test -statistics?
  2. Give an example of a typical situation where this test statistic will be appropriate
  3. A formula for calculating a chi-square contigency test statistics is given as

X^{2}=sum_{i=1}^{r} sum_{j=1}^{c}frac{(o_{ij}-e_{ij})^{2}}{e_{ij}}  with d.f=(r-1)(c-1)

o_{ij}= observed frequency in cell(i,j)

e_{ij}= expected frequency in cell(i,j)

r= number of rows

c=number of columns

Using the data presented below calculate a chi-square contigency test statistic for variable X and Y

Variable (X) Variable (Y)
Y11 Y12
X11 12 108
X12 24 156
  1. Test the hypothesis that X is independent of Y at alpha (alpha)=5%. Note that x^{2}.05=3.841
  2. What is your conclusion at this level of significance?

Mathematical Calculation
2

A confidence interval is calculated as ar{x}pm Z_{frac{alpha}{2}}frac{sigma }{sqrt{n}}. A researcher from Mzumbe University observed that in a sample of 28, the mean was 1.68 and sample variance was 0.71

  1. Construct a 95% confidence interval for mu. Assume that the sample was drawn from a normal distribution. Note that t_{frac{alpha}{2}}=2.064
  2. What is the meaning of this confidence interval?
  3. Another researcher claims that the population mean is 2.5. At this level of significance.
  1. State the null and alternative hypothesis
  2. Test the null hypothesis.

Mathematical Calculation
3

The OLS fitted line explaining college GPA in terms of high school GPA and ACT score is estimated as:

ColGPA=1.29+0.453GPA+0.0094ACT

  1. Interpret the intercept and slope coefficient
  2. Using the information provided above , complete the following table
Observed value of college GPA 3.4 3.5 3.6 2.8 3.1 2.9 2.8 2.5
Predicted value of college GPA                
GPA 3 3.2 2.8 2.6 2.9 3.5 3.8 3.9
ACT 24.2 25.6 25.8 26 26.2 26.4 26.6 26.8
Predicted error                

 


Mathematical Calculation
4

Use the information provided in the table below to answer questions that follows

Observed data for variables X and Y

Observation No Observed values of X Observed values of Y
1 2 4
2 4 6
3 5 8
4 7 9
5 8 12
6 11 16
7 13 21
8 15 17
9 16 20
10 19 25
  1. Calculate the estimators of alpha (alpha) and Beta(eta) in the folowing regression model

y=alpha +eta x + varepsilon

hat{alpha}=ar{y}-hat{eta}ar{x}

The estimators can be calculated as hat{eta}=frac{sum(x_{i}-ar{x})(y_{i}-ar{y})}{sum(x_{i}-ar{x})^{2}}

  1. State the null and alternative hypothesis that arre needed to test whether the slope coefficient is zero.

Mathematical Calculation
5

What is the meaning of the following terminologies / concepts as used in econometrics

  1. Asymptotic unbiasness
  2. Asymptotic efficiency
  3. Serial correlation
  4. Logistic regression
  5. Heteroskedasticit

Short answers
6

Suppose we have two independent sets of data with sample size n_{1} and n_{2} respectively. The regression equation is

y=alpha_{1}+eta_{11}X_{1}+.....+eta_{1k}X_{k}+mu

for the first(1st ) data set and

y=alpha_{2}+eta_{21}X_{1}+.....+eta_{2k}X_{k}+mu

for the second (2nd ) data set

Note that for the eta`s the 1st subscript denotes the data set and the second subscript denoted the variable.

  1. Write the null and alternative hypothesis to test whether the data betweeen the population that generated the two data sets is stable.
  2. The test statistic for the stability test is:

F=frac{frac{RRSS-URSS}{k+1}}{frac{URSS}{n_{1}+n_{2}-2k-2}}approx F[(?),(?)]

Where RRSS is the restricted sum od squares (obtained from the regression with poled data) and URSS is the unrestricted sum of squares (obtained from the two separate regression). What are the degrees of freedom for this test statistic?

  1. If the test statistic calculated in (b) above is greater than the tabualted value what would you conclude?

Mathematical Calculation
7
  1. Using your knowledge ANOVA complete all the missing values in the table below:

Analysis of variance for a simple regression model.

Source of variation Sum of square(SS) Degree of freedom (df) Mean square (MS)=(SS/df) F-statistic
Regression(ESS) 150.75      
Residual (RSS)   8    
Total(TSS) 300.40 9    
  1. Explain the significance of the F-statistic presented in the above table
  2. Using your own knowledge , explain why the test statistic in the ANOVA is in F-statistic
  3. Given this F-test what are numerators and denominators degree of freedom?

Mathematical Calculation
8

An analyst wants to model technology adoption(TECH) among small scale farmers as function of age(AG), education level(EDUC) and disposable income(INC). Technology adoption is a binary variable and is defined as:

TECH=left{egin{matrix} 1 ,if, a, farmer, adopts, the , technology & \ 0 , if, a, farmer, does, not, adopt, the, technology& end{matrix} ight.

  1. Specify an appropriate regression model for technology adoption
  2. Explain if it is possible to estimate the relationship specified in part(i) using the ordinary least square (OLS) method.
  3. If it is not possible to use the OLS method what will be the alternative model that you will estimate?
  4. What will be the distribution of the errors in the model you recommended in part(ii) above?

Short answers
9

Observed values of Y and X.

Observation No 1 2 3 4 5 6 7 8 9 10 11
Variable Y 3.00 3.41 3.73 4.00 4.24 4.45 4.65 4.83 5.00 5.16 5.32
Variable X 1.00 1.21 1.35 1.46 1.56 1.64 1.71 1.77 1.83 1.88 1.93

Note that the intercept of the regression line (alpha)=ar{Y}-bar{X}

The slope coefficient (eta)=frac{sum_{i=1}^{n}(X_{i}-ar{X})(Y_{i}-ar{Y})}{sum_{i=1}^{n}(X_{i}-ar{X})^{2}}

  1. What is the approximate value of the slope coefficient for this regression model?
  1. 2.00
  2. 2.52
  3. 2.98
  4. 3.50
  5. 5.01
  6. None of the above
  1. What is the approximate value of the intercept for this regression model?
  1. 0.15
  2. 0.35
  3. 0.71
  4. 0.27
  5. 0.37
  6. None of the above

 


Multiple choices
10

ANOVA

  df SS MS F Significance F
Regression 1 5.54 PP AS 0.00
Residual 9 0.03 QQ    
Total 10 5.57      
           

What is the approximate value of PP?

  1. 5.00
  2. 5.30
  3. 5.23
  4. 5.54
  5. 5.08
  6. None of the above

Multiple choices