ME Individual 1

a) Using any computer software, perform regression analysis from the data in the Table.
The following is the regression analysis on data given by using Microsoft Excel:
Regression Statistics

Multiple R
0.986557829

R Square
0.973296349

Adjusted R Square
0.968845741

Standard Error
184.7121318

Observations
15

ANOVA

df
SS
MS
F
Significance F

Regression
2
14922670.21
7461335
218.68838
0.00000000036260

Residual
12
409422.8596
34118.6

Total
14
15332093.07

Coefficients
Standard Error t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
130.3768645
106.9609698
1.21892
0.2462943
-102.6710688
363.4247979
-102.671069
363.424798
LABOR
2.327893582
0.671739122
3.46547
0.0046698
0.864299765
3.791487398
0.86429977
3.7914874
CAPITAL
0.397539958
0.083656327
4.75206
0.0004705
0.215268479
0.579811437
0.21526848
0.57981144

b) From the result of the regression analysis, write the function in linear form.
Y = α + α1L + α2C + ε α = 130.377 α1= 2.328 α2= 0.398
Substitute α, α 1, α 2 into the production function,
Y = 130.377 + 2.328L + 0.398C

c) Test whether the coefficients of capital and labor are statistically significant.

F-test
The F-value is 218.688. So, we reject the null hypothesis and conclude that the independence variables are useful in explaining the sale of LOAF with (1-0.00000000036260) = 99.99% confidence at 0.05 significant level. t-test The t-value for labor is 3.465 and capital is 4.752 (i.e. greater than 2 in absolute value). Hence, we can conclude that both labor and capital are statistically significance in explaining the sales of LOAF.
P-value
From the Table, the P-value for the estimated coefficient of labor is 0.005 and capital is 0.0005.
This means, there is only 0.5 in 100 chance that the true coefficient of labor is actually 0 and there is only 0.05 in 100 chance that the true coefficient of