Question

Consider the following estimated equation QOL - 2.07 + 0.81 WB+ 0.33 MW + 0.12 RM (2.015) (0.421) (0.012) (6.065) n = 100, R? -0.79, R = 0.778 where QOL represents quality of life, WB represents well-being, MW represents log of minimum wage and RM represents log of remittances. QOL and WB are measured on a scale from 0 to 100 percent, while MW and RM are measured in dollars. Standard errors are in parentheses. (a) Interpret the coefficient on RM (2 marks (b) Interpret R2 [2 marks] (c) Holding MW and RM fixed at 0, what is quality of life predicted to be if well-being is 5%? [3 mark] (d) Test the null hypothesis that the coefficient on MW is one against the alternative that the coefficient is less than one. 15 marks (e) Test the null hypothesis that the coefficient on RM is zero against the alternative that the coefficient is greater than zero at the 1% level. 15 marks () Test the overall significance of the model 15 marks

Answer 1

Equation :

QOL = 2.07 + 0.81 WB +0.33MW +0.12 RM

n = 100, R²=0.79

a). Interpretation:

If RM increase by 1 unit or 100% then there is an incease of 0.12 units or 12% increase in QOL

b). R² = 0.79 meaning that all these variables WB, MW, RM explain 79% variability in QOL.

c). If WM is 5%, then WB = 5

and holding other variables constant we have:

QOL = 2.07 + 0.81*5 = 6.12 is the quality of life

d). For MW, beta = 0.33 and SE = 0.012

Now, Ho: $\beta_2 = 1$ vs H1: $\beta_2 <1$

Then, $t = \frac{\hat\beta_2 - \beta_2}{SE_{\hat\beta_2}}$ ~ t(98, 0.05)

t = (0.33-1)/0.012 = -55.33

Then, |t| > t(98,0.05)

We reject Ho or can say that coefficient on MW is less than 1.

e). Similarly,

t = (0.12)/(0.065) = 1.846

then, t(98,0.01) = 2.33

Here, t < t(98,0.01) we fail to reject Ho or can say that coefficient on RM is equal to 0.

f). More details are required

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