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(2938) Question Category: Mathematical Calculation

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?

Answer / Solution

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(2939) Question Category: Mathematical Calculation

  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?

Answer / Solution

UNSOLVED

(2967) Question Category: Short answers

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?

Answer / Solution

UNSOLVED

(2968) Question Category: Multiple choices

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

 

Answer / Solution

UNSOLVED

(2969) Question Category: Multiple choices

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

Answer / Solution

UNSOLVED

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