Question

In his study on the labor hours spent by the FDIC (Federal deposit insurance Corporation) on 91 bank examinations, R.J. Miller estimated the following function.
lnY=2.41+0.3674lnX1+0.2217lnx2+0.0803lnx3-0.1755D1+0.2799D2+0.5634D3-0.2572D4
(0.55) (0.0477) (0.0628) (0.0287) (0.2905) (0.1044) (0.1657) (0.0787)
R2=0.766
Where Y= FDIC examiner labor hours
X1= Total assets of bank, x2 total number of offices in bank, x3 ratio of classified loans to total loan for bank . D1=1 if management rating was good D2=1 if management rating was fair D3=1 if management rating was satisfactory D4=1 if examination was conducted jointly with the state.
a)   Interpret the results
b)   Interpret the dummy variables
c)   Which of the parameters from the estimated regression are statistically significant at 5% significance level?

Answer 1

Here the multiple linear regression model is given by,

lnY=2.41+ 0.3674lnX1+ 0.2217lnx2+ 0.0803lnx3- 0.1755D1+ 0.2799D2+ 0.5634D3- 0.2572D4

(0.55) (0.0477) (0.0628) (0.0287) (0.2905) (0.1044) (0.1657) (0.0787)

Here the number in the parenthesis gives the p-value.

where, Y= FDIC examiner labor hours
X1= Total assets of bank,

x2 = total number of offices in bank,

x3 = ratio of classified loans to total loan for bank

D1= 1 if management rating was good

D2=1 if management rating was fair

D3=1 if management rating was satisfactory

D4=1 if examination was conducted jointly with the state.

Interpretation:

i) Here in this model logY has been predicted by logX1, logx2, logx3, D1, D2, D3 and D4 where descriptio of the variables atre writen above.

ii) Interpretation of the coefficients of the model:

a)Here intercept of the model is 2.41, which tells us, when all the variables used in the model has value zero then what would be the value of lnY. Here, in the model log of some variables has been used as predictors. So, log of those variable equal to zero means value of the variable is essentially 1.

b) coefficient corresponding to variable lnX1 is 0.3674. It tells us that, if lnX1 is increased by a unit keeping all other regressor variables fixed lnY would increase by 0.3674.

c) coefficient corresponding to variable lnx2 is 0.2217. It tells us that, if lnx2 is increased by a unit keeping all other regressor variables fixed lnY would increase by 0.2217.

d) coefficient corresponding to variable lnx3 is 0.0803. It tells us that, if lnx3 is increased by a unit keeping all other regressor variables fixed lnY would increase by 0.0803.

e) coefficient corresponding to D1 is -0.1755. It tells us that if managegement ratings were good(D1=1) instead of bad (D1=0), lnY would decrease by 0.1755.

f) coefficient corresponding to D2 is 0.2799. It tells us that if managegement ratings were fair(D2=1) instead of unfair (D2=0), lnY would increase by 0.2799.

g) coefficient corresponding to D3 is 0.5634. It tells us that if managegement ratings were satisfactory(D3=1) instead of unsatisfactory (D3=0), lnY would increase by 0.5634.

h) coefficient corresponding to D4 is -0.2572. It tells us that if the examination was conducted jointly with the state(D4=1) instead of was not conducted jointly with the state (D4=0), lnY would decrease by 0.2572.

iii) R² of the model is 0.766, which tells us that 76.6% variability in the data has been captured by the model. So, the performance of the model is quite satisfactory with respect to R².

iv) From the values in the parentheses we can observe that, the p-values corresponding to lnX1 and lnx3 are less than 0.05. So, these parameters are significant at 5% level.

[Note:

We are getting this p-values corresponding to the test, H₀: parameter = 0 against H₁: parameter 0

If p value is less than 0.05, then have to reject H₀ at 5% level and we will conclude that that parameter is significant.]