Question

For a sample of USA industries the following variables are recorded:

YOUTPUT is the total production of each industry in millions of dollars in constant prices.

WAGES corresponds to the total wages of the each industry in millions of dollars in constant prices.

KCAPITAL is the fixed capital of each industry in millions of dollars in constant prices. Labor is the total number of employees in each industry in thousands.

D1 is a dummy variable which takes the value of 1 when a manufacturing industry is technologically advanced and 0 otherwise.

D2 is a dummy variable which takes the value of 1 when a manufacturing industry is profitable and 0 otherwise.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0,887697
R Square	0,788006
Adjusted R Square	0,785736
Standard Error	14470,28
Observations	473
ANOVA
	df	SS	MS	F	Significance F
Regression	5	3,63E+11	7,27E+10	347,1789	9,4E-155
Residual	467	9,78E+10	2,09E+08
Total	472	4,61E+11
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95,0%	Upper 95,0%
Intercept	192,2124	1250,783	0,153674	0,877933	-2265,65	2650,073	-2265,65	2650,073
WAGES	13,81387	0,913179	15,12723	2,33E-42	12,01942	15,60832	12,01942	15,60832
KCAPITAL	-0,33749	0,075055	-4,49658	8,72E-06	-0,48498	-0,19	-0,48498	-0,19
Labor	-240,151	31,17609	-7,70306	8,02E-14	-301,414	-178,888	-301,414	-178,888
D1	-221,005	1391,105	-0,15887	0,87384	-2954,61	2512,595	-2954,61	2512,595
D2	5838,63	1562,002	3,737914	0,000209	2769,207	8908,054	2769,207	8908,054

Based on the data described above, the main research question at hand is the following:

“How industrial production is affected by the level of labor, wages, capital, profitability and technology”

1. Having in mind the main research question, estimate a linear regression model including all the explanatory variables, using the least squares method.

2. Give the interpretation of the regression coefficients of the selected model.

3. Estimate a new model without the insignificant explanatory variables.

4. For the selected model in 3 calculate the coefficient of determination and give its interpretation in terms of the given research question.

Answer 1

1) Linear regression model:
YOUTPUT = Intercept + WAGES + KCAPITAL + Labor + D1(0 or 1) + D2(0 or 1)

2) high value of intercept means that even without the factors, the output is high
wages is positively related with output i.e higher the wages, higher is the output,
whereas capital and labor are negatively related i.e higher the capital/ labor, lower is the output
D1 and D2 takes the value of 0 and 1, the significance of D1 and/or D2 means that there is a significant difference in the coefficients between the two groups

3) at 5% significance level, if the p-value is lower than 0.05, the variable is significant else not
YOUTPUT = WAGES + KCAPITAL + Labor + D2(0 or 1)

4) coefficient of determination = R square = 0.788006
R square represents the goodness of fit i.e how close are the original values to the linear estimates. It represents the ratio of the variance in the dependent variable that is predictable from the independent variable. In terms of the research question, it means that the given independent variables are good predictors for the research question as R square is acceptably high.