Question

	coefficient	standard error	t-test	p-value
intercept	-70.49511	12.69501	-5.55298	1.76E-07
x1	0.00474	0.00011	43.22597	3.41E-74
x2	0.00363	.00106	3.4366	0.00814
x3	0.28008	0.12949	2.16301	0.032557
x4	0.78346	0.16579	4.72566	6.39E-06

R^2=0.94, F-statstic=35.92, p-value of the F stat=9.73E-73

A.the validity of the entire model at 5% significance level

B.interpretation of R^2

C. stastical significance of the coefiicients at 5% significant level

D. Verbal interpreation of the effect of each coefficient on the dependent variable

E. suggestions on reducing the cost of production.

Answer 1

1. Since the model has p-value of the test statistic 3.73E-73 which is very very small, we conclude that model is highly significant. Hence at 5% significance level, the model is significant as p-value <<< 0.05
2. The = 0.94 meaning that model is able to capture and explain 94% of the total variation in the data through independent variable.
3. At significance level 5%, we see that p-value of all the variable including the intercept is <0.05 which suggests that all the variables in the model are significant. So all the coefficients are significant in explaining the dependent variable
4. The interpretation of coefficients of each variable: E.g. Coefficient of the variable X4 is 0.78346 which implies that for a unit change in the X4 variable, the change reflected in the dependent variable due to this change is 0.78346. Likewise the interpretation of all the coefficients are same.

Thanks