The Coefficient for Noroom - Coursework Example

Question 1
Model2
(Model 2) read = 419.7 – 18.6 * no room – 50.0 * noting + 29.4 * fiction
N = 11984, R2 = 0.204
(1.7) (2.6) (3.1) (0.6)
Interpretation of the coefficient for Noroom
Because no room is one of the continuous variables, its coefficient is represented by -18.6 which is a constant. If the value of no room increases, the model value reduces
Hypothesis test
In order to test for the hypothesis, we use a t-test as follows


t = (1.7-2.6)/(3.1/SQRT(18.6)) =
The t score is less than 0.5 at the 5% significance level (Dougherty, 2008). This confirms the null hypothesis, that the parameter is -20 against the alternative hypothesis that the parameter is greater than -20.
Question 2
The question is whether students whose home language is not English are more or less eager readers of fiction than those who speak English at home.
The null hypothesis is that the students whose language is not English are not more eager readers of fiction than those who speak English at home. The alternative hypothesis is that the students whose language is not English are more eager readers of fiction than those who speak English at home. The t-test in this case is as follows:



t = (0.6-3.1)/ (2.6/SQRT (50))
t = -6.7991

The t score is less than 0.5 at the significance level; hence the score is highly positive (Wooldridge, 2012). The null hypothesis that students whose language is not English are not more eager readers of fiction than those who speak English at home is therefore proved false, against the alternative hypothesis. The alternative hypothesis that the students whose language is not English are more eager readers of fiction than those who speak English at home, is proven to be true.
Question 3
If we run 'Model 3' where fiction is replaced with fic2, fic3, fic4, and fic5,
the interpretation of the estimated coefficient for fic3 would be as follows:
If fiction is replaced by fic1, fic2, fic3, fic4, and fic5, there would be a coefficient estimated incremental values of read. The coefficients of fic3 are estimated as shown below:
Fic 1 = 29.4 * 0.204 = 5.9976
Fic 2 = 29.4 * 0.204 * 2 = 6.2016
Fic 3 = 29.4 * 0.204 *3 = 17.9928
The coefficient is growing incrementally. This shows that as model 3 is run with different coefficients, the eagerness to read fiction increases.
The model will become as follows:
(Model 2) read = 419.7 18.6*noroom 50.0*noeng + 29.4*5.9976 N = 11984, R2 = 0.204
(1.7) (2.6) (3.1) (0.6)
(Model 2) read = 419.7 18.6*noroom 50.0*noeng + 29.4*6.2016 N = 11984, R2 = 0.204
(1.7) (2.6) (3.1) (0.6)
(Model 2) read = 419.7 18.6*noroom 50.0*noeng + 29.4*17.9928 N = 11984, R2 = 0.204
(1.7) (2.6) (3.1) (0.6)
Question 4
What could happen to R2 in the hypothetical 'Model 3'? Be as precise as you can
In the hypothetical model, R2 will increase as the number of regressors increases from 1 to 5.
Minimizing the residual value of the sum of squares will maximize the value of R2 so that the optimization problem does not provide a coefficient that is less than or greater than zero. The values of R2 increase in the sequence shown below:
In the first equation of Model 2
R2 = 0.204 * 1 = 0.0204
In the second equation of Model 2
R2 = 0.204 * 2 = 0.0408
In the third equation of Model 2
R2 = 0.204 * 3 = 0.1224
Question 5
If there was only one variable for the regression model, it would be logical to use the variable with the greatest coefficient to maximize the power of the model. In this case, for all the models, we use long as the variable for maximizing the powers of the models. This is because doing has the greatest coefficient in all the models. Read More