ECON2900Y nt and dependent variables n A researcher is analysing the relationshi

Question

ECON2900Y nt and dependent variables n A researcher is analysing the relationship between the independe sngaession model. She has estimated her first model from a samplie of 204 observations 5% level of significance: s,s = 4 RA2 -0.65 bles Also, she has developed a correlation matrix for her three independent varia Xs -0.1 0.1 1.0 Correlation Matrix Xt -0.1 -0.1 -0.1 1.0 0.1 Based on the correlation results, she has then applied the forward selection search procedure based not only on significance but also on goodness of fit. She believes goodness of fit is the Rey element in building models Using a 5% level of significance she has selected her final model from a sample of 203 observations: Y =10+10X1 + 10X2 S01 = 1 RA2 = 0.90 a) Was a search procedure necessary? Why? b) Forecast the value of Y when X1 = 10, X2-10 and X: 10? c) Forecast the value of Y when X 1 and X2 1? d) Can you explain 90% of the behaviour of Y, using X, X2 and Xs altogether? e) Can you explain 65% of the behaviour of Y, using X1 and X2 altogether? 20 points

Explanation / Answer

b).

Consider the given problem, here we have given 2 estimated regression model, these are given by, Y = 10 – 2*X1 – 4*X2 – 8*X3, with R^2=0.65=65%.

So, if X1=10, X2=10 and X3=10, then the estimated value is given by “Y = 10 – 2*10 – 4*10 – 8*10 = 10 – 20 – 40 – 80 = 10 -140 = (-130),

so the estimated value of “Y” is given by “(-130)”.

c).

Now, the 2nd model is given by “Y = 10 + 10*X1 + 10*X2”, so if X1 = X2 = 1, => Y = 10 + 10*1 + 10*1 = 30,

=> Y = 30.

So, here the estimated value of “Y”, is given by “Y=30”.

d).

Now, if we explain the behavior of “Y”, by using X1, X2 and X3 together then we need to consider the 1st model, where “Y” be the dependent variable and X1, X2 and X3 be the independent variables. So, here the R^2=0.65=65%, => the given model is able to explain “65%” variation in “Y” and the rest is still remain unexplained.

e).

Now, if we explain the behavior of “Y”, by using X1, X2 and together then we need to consider the 2nd model, where “Y” be the dependent variable and X1, X2 and be the independent variables. So, here the R^2=0.9=90%, => the given model is able to explain “90%” variation in “Y” and the rest is still remain unexplained.

So, if we compare these 2 models then we can see that the 2nd one is more appropriate, since it can able to explain more variation in “Y”, compared to the 1st model.

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