Question

You were asked by your manager to evaluate the regression tables below to decide which cost driver would be best to use for the production department. Since your manager is new and does not understand the regression analysis tables, you will need to explain why one set of statistics is better than the other and why you have chosen the better driver.  

Manufacturing Direct Labor Hours
Regression Statistics
Multiple R	0.799304258
R Square	0.638887297
Adjusted R Square	0.602776026
Standard Error	937.1853461
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	1	15539336.27	15539336	17.69218558	0.001810776
Residual	10	8783163.73	878316.4
Total	11	24322500
	Coefficients	Standard Error	t Stat	P-value
Intercept	1532.330232	2190.385348	0.699571	0.500144187
OH Costs	0.038428034	0.009136028	4.206208	0.001810776

Manufacturing Machine Hours
Regression Statistics
Multiple R	0.868515979
R Square	0.754320006
Adjusted R Square	0.727022228
Standard Error	29.94755517
Observations	11
ANOVA
	df	SS	MS	F	Significance F
Regression	1	24782.84091	24782.84	27.63302	0.000523013
Residual	9	8071.704545	896.8561
Total	10	32854.54545
	Coefficients	Standard Error	t Stat	P-value
Intercept	114.6704545	88.29220603	1.298761	0.226313
Units	0.053068182	0.010095319	5.256712	0.000523

Answer 1

The regression in 2nd table "Manufacturing Machine Hours" is better than regression in 1st table "Manufacturing Direct Labor Hours" because of below reasons

1) the correlation coefficient (Multiple R) is larger, and R Square is 0.754320006 in 2nd regression analysis which means 75% variation is explained by the model by 2nd regression analysis, where as R Square is 0.638887297 in 1st regression analysis i.e. only 63% variation is explained by the model.

2) The global F test (ANOVA table), Significance F is smaller in 2nd regression analysis

3) P-value is smaller for tests for slope (0.000523 for 2nd regression analysis)