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Econometrics questions.

Econometrics questions.

Find Econometrics university examination questions in acaproso.com

# Question
1

A farmer wishes to predict the number of tons of maize per acre which will result from a given number of applications of fertilizer. Data have been collected as shown in the table below:

Fertilizer application 1 2 4 5 6 8 10
Tons of maize per acre 2 3 4 7 12 10 7
  1. Find a suitable regression relationship to help the farmer in making the required prediction
  2. From your results predict the number of tons per acre resulting from 0,3,7 and 9 applications.

Mathematical Calculation
2

Suppose you are involved in a research project aiming at establishing the influence of an independent variable (XVAR) on a dependent variable (YVAR). One of your collagues is the project team member who was conversant with SPSS helped to run the analysis and produced estimation results summarized in three tables below.

SPSS output

Table 1: Model Summary

Model R R Square Adjusted R Square Std.Error of the Estimate
1 .929(a) .862 .845 1.19149
  1. Predictors: (Constant), xvar

Table 2: ANOVA(b)

  Sum of squares df Mean Square F Slg.
Regression 71.143 1 71.143 50.113 .000(a)
Residual 11.357 8 1.420    
Total 82.500 9      
  1. Predictors: (Constant), XVAR
  2. Dependent Variable: YVAR

Table 3: Coefficients (a)

  Unstandardized Coeff. Standardized Coeff. t Sig.
  B Std.Error Beta    
(COnstant) -2.639 1.210   -2.181 .061
XVAR .554 .078 .929 7.079 .000
  1. Dependent Variable :YVAR

Suppose this SPSS output was given to you , asnwer the following questions:

  1. How many variables were dependent and how many were independent?
  2. What was the explanatory power of the regression model?
  3. It seems the regression model was not robust in fitting the relationship, is this true or false? If true or false explain why?
  4. Was the parameter estimate for XVAR statistically significant or not? If it is significant , at what significance level (statistically plausible level is P<5%) or if it is not, explain why?
  5. Suppose the YVAR is the household monthly consumption and XVAR is disposable monthly income? Discuss briefly the SPSS results of the model.

Mathematical Calculation
3

Cost of production have been monitored for some time within an agribusiness firm and the following data found:

Production level (`000s) Average total cost (Tshs `000)
1 70
2 65
3 50
4 40
5 30
6 25
7 20
8 21
9 20
10 19
11 17
12 18
13 18
14 19
15 20

Answer the following questions:

  1. Develop mathematical and econometric models relating average total cost and production level
  2. Find the regression line of average total cost on production level
  3. Place the estimated regression line on the scatter plot
  4. COmpute the coefficient of determination, R-Squared and interpret  it
  5. Test the significance of the regression coefficient attached to independent variable (x), i.e if it is non-zero
  6. Predict the average total cost if the production level were i)8500 units ii)16000 units  iii) 20000 units

Mathematical Calculation
4

To ease presentation econometric concepts are always stated using mathematical formula. State the meaning of the following formula.

  1. y_{i}=alpha + eta x_{i}+varepsilon _{i}
  2. E(varepsilon _{i})=0
  3. Var(varepsilon _{i})=sigma ^{2}
  4. Cov(varepsilon _{i}, varepsilon _{j})=0
  5. varepsilon _{i}sim Normal

Mathematical Calculation
5

Manufacturing output for palnt A and B

Unit output (Plant A) 15 25 35 20 30
Unit output (Plant B) 23 26 25 24 27

Using the data in the table above calculate

  1. The expected output for plant A and B
  2. The sample variance for plant A and B
  3. Based on these output statistics which plant has a stable production? Why ?

Mathematical Calculation
6

You have been requested to estimate the relationship between the exchange rate (S_{t}) the interest rate (r_{t}). Econometrically, a model for the exchange rate as a function of the interest  rate is given as:

S_{t}=alpha +eta r_{t}+e_{t}

Note that the subscript stands for time in which the data were observed

  1. What is the interpretation of the regression coefficients
  2. What type of data is used is in this model?
  3. What problem is most likely to be encountered upon estimation?
  4. How will you test the presence of this problem
  5. In an event you detect the problem identified in part (d) what will you do to fix it?

Mathematical Calculation
7

Read the data presented in the table below

Data on tree height and trunk diameter.

Tree Height (Y) 35 49 27 33 60 21 45 51
Trunk Diameter (x) 8 9 7 6 13 7 11 12

r=frac{nsum xy- sum xsum y}{sqrt{[n(sum x^{2})-(sum x)^{2}][n(sum y^{2})-(sum y)^{2}]}}

Note that t has  n-2 degrees of freedom

  1. Using data presented above, calculate the sample correlation coefficient between tree height and trunk diameter
  2. Interpret the correlation coefficient
  3. State the null and alternative hypothesis to test whether there is a significant linear relationship between y and x.
  4. What conclusion will you make? Note that t(6)=2.4469

Mathematical Calculation
8

Probit and logit are typical examples of non-linear probability models.


True OR False
9

When a logit model is estimated an analyst assumes that errors are normally distributed with a known mean and known variance.


True OR False
10

A distribution is skewed  to the right when: mean <median<mode.


True OR False