Answer to Question #233002 in Statistics and Probability for Godiya

Question

1) A researcher obtained the following ordinary least squares (OLS) estimates for a

Nigerian firm’s stock price using 120 observations from 2010 m1 to 2019m12 (All

variables in logarithms):

R2 = 0.34, RSS = 1.24, F4 115= 3.75

ln st = 0.87 - 0.54ln pt + 0.65ln yt + 0.34ln rt - 0.32ln mt

(1.06) (0.24) (0.30) (0.12) (0.24)

st are the log of the stock price, pt is the log of profits, yt is the log of its output in the Nigerian,

rt is the log of expenditure on research and development and mt is the log of expenditure on

Marketing. Figures in parentheses are standard errors and RSS is the Residual Sum of Squares.

i) Briefly evaluate the reasons behind including the above explanatory variables in

the regression.

ii) What is the explanatory power of the regression?

iii) Individually using the t-test, test whether each coefficient equals 0, at the 5% level

of significance

iv) Using a t-test does the coefficient on the variable lnyt = 1?

Answer 1

i)

From the given information, the regression equation is given by

$\ln S_t = 0.87 -054 \ln p_t + 0.65 \ln y_t + 0.34 \ln r_t - 0.32 \ln m_t$

The relation between stock price and the profit, expenditure on marketing are negatively related, because the coefficient of the corresponding variables of regression equation show negative signs The relation bethmen stock price and output, expenditure are positively related.

 

ii)

From the given information, p is the log of profit, y is the log of its output in Ghana_ The stock price depends on the profit and output percentages. 

iii)

The explanatory power of the regression can measure by the coefficient of determination. In multiple regression cases, the adjusted Rxquare value gives the approximate efficiency to the regression model Her; the adjusted R-square value is = 034. It means that all independent variables explain 34% of the variation in stock price. The rest of 66% of the variation in stock price is not explained by Mean independent variables. 

iv) Calculate the test statistics and Pyalues of each coefficient in the model as follows:

$df=(n-k-1)=(120-4-1)=15$

k is the number of explanatory variables 

From the above table, observe the Ptalues.

The P-value of the y_t and r_t is less than the level of significance 0 05, i.e. (0 0054< 005) and (0 0078 < 0 05). Thus, the researchers reject the null hypothesis that the explanatory variable does not significantly affect the regression model.