ETF2100/5910: Regression Model by Least Squares - Econometrics Assessment Answer

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ETF2100 Regression Model by Least Squares -
Econometrics Assessment Answer
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• Question 1 - Econometrics Assignment Help
  Australia
• (a) Estimate the following regression model by
  least squares. Report the result in full. No need
  to provide Eviews output here. 
• ln(price)i ß1 ß2bedi ei (A1)
• (b) Interpret the estimated slope coefficient. Be
  careful about the unit in your interpretation. Is
  the sign of the slope coefficient what you
  expected? Why? (2 marks)

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• (c) Your friend commented on your result above
  that your model might incorrectly leave out the
  size of each house (sqft) and that can have
  consequences on your estimate of ß2. Do you agree
  with your friends comment? Why or why not? What
  would be the consequence of omitting the variable
  sqft? 
• (d) Now estimate the following model where we add
  in house size. Report the result in full AND
  provide Eviews output here.
• ln(price)i ß1 ß2bedi ß3sqfti ei (A2)
• (e) Interpret b2, your estimate for ß2 from part
  (d). How does this interpretation differ from the
  interpretation in part (b)
• (f) Using model in (A2), is there evidence that
  the number of bedroom has an effect on ln(price)?
  Note p-value approach is sufficient for this
  part. 

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• (g) Compare the coefficient for bed that you got
  from estimating model (A1) and from model (A2).
  Which one of these two estimates is more
  reliable? If you think one of these estimates is
  biased, explain which one and why. In that case,
  what is the direction of the bias based on your
  comparison of the two estimates?
• (h) Using Eviews, find and report the (Pearson)
  correlation coefficient between bed and sqft. Is
  the sign what you expected?(i) Does what you
  find in part (h) and any other previous parts
  support your answer in part (g), in particular
  with regard to the direction of the bias? Explain 

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• Question 2 (a) Now consider the following model.
  Explain the reason why we include the variables
  age and age squared in the model. 
• ln(price)i ß1 ß2sqfti ß3agei ß4age2
• i ei (A3)
• (b) Report the result in full and provide Eviews
  output (c) Using the F-test at 5 significance
  level, test whether age helps explain variation
  in house prices. You must write out the test in
  full including null and alternativehypotheses
  stated in terms of the parameters. Compute the
  F-statistic manually by estimating both the
  restricted and unrestricted model. 

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• (d) What do the estimates for ß3 and ß4 tell you
  about the relationship between house price and
  house age, keeping size constant. Hint Think
  about the signs of these coefficients and what
  they say about the shape of the quadratic
  function. Make sure to explain your answer in the
  context of the question. 
• (e) Write down the expressions for ?E(ln(price) \
  X) ?agewhere X denote all observations on sqft
  and age. Interpret this expression for a house
  with age equal to a particular level, say age0.
  Be careful about the use of units and
  percentages. Note, there is no need to put in any
  numbers here and you can use bk to denote
  estimate for ßk.

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• (f) Using the F-test at 5 significance level,
  test the null hypothesis that houses start
  becoming more expensive with age when they are 50
  years old. You must write out the test in full
  including null and alternative hypotheses stated
  in terms of the parameters. Compute the
  F-statistic manually by estimating both the
  restricted and unrestricted model. 
• (g) Find point prediction (using the corrected
  predictor) AND 95 prediction interval for the
  price of a 45-year old house with 2000 square
  feet living area.

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• Question 3
• Now estimate the following model using least
  squares. Report the result in full AND provide
  Eviews output.  pricei ß1 ß2sqfti ß3agei
  ß4bathsi ei (A4)
• Interpret the estimated coefficient for sqft, age
  and baths. Is the sign of each coefficient what
  you expected? Why? 
• Construct a 99 interval estimate for ß4.
  Interpret this interval estimate. 
• Test at the 5 level of significance the null
  hypothesis that an increase in total living area
  by 100 square feet has the same effect on house
  price as a 10 year decrease in the house age,
  other things being constant. Use a t-statistic
  approach and write down all the steps used to
  conduct your test.

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• (e) You suspect that the change in price
  associated with an extra square feet of house
  size depends on how old the house is. Extend the
  model in (A4) to allow for this (write the new
  model down). Estimate this model and include your
  Eviews output.
• (f) Comment on the significance of all the
  coefficients in the extended model you estimate
  in part (e) using the p-value approach.
• (g) Using this extended model, write down the
  expressions for the marginal effect ?E(price \X)
  ?sqft where X denote all observations on sqft and
  age. Interpret this expression for a house with
  age equal to a particular level, say age0. Note,
  there is no need to put in any numbers here and
  you can use bk to denote estimate for ßk. 

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• (h) Find point estimates AND 95 interval
  estimates for the marginal effect of an extra
  hundred square feet of total living area on house
  price for houses that are (i) 2 years old, and
  (ii) 45 years old. How do these estimates change
  as age increases? (i) Using model in (A4),
  perform RESET tests with one and two terms. Do
  the tests suggest that the model is a reasonable
  one? 

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