Question

QUESTION 12

1. A Director of Human Resources is exploring employee absenteeism at a Hospital. A multiple linear regression analysis was performed using the following variables. The results are presented below.

   Variable	Description
   Y	number of days absent last fiscal year
   x1	commuting distance (in miles)
   x2	employee's age (in years)
   x3	length of employment at PPP (in years)

   	Coefficients	Standard Error	t Statistic	p-value
   Intercept	6.594146	3.273005	2.014707	0.047671
   x1	-0.18019	0.141949	-1.26939	0.208391
   x2	0.268156	0.260643	1.028828	0.307005
   x3	-2.31068	0.962056	-2.40182	0.018896

   R=0.498191	R2=0.248194	Adj R2=0.192089
   se = 3.553858	n = 73

   Which of the following statements is correct about the R2?

   	a.	The adjusted R2 value is 0.25. This means that the model explains around 25% of the variation in the average number of days absent in the last year.
   	b.	The adjusted R2 value is approximately 0.19. This means that the model explains around 19% of the variation in the average number of days absent in the last year.
   	c.	The adjusted R2 value is 0.50. This means that the model explains around 50% of the variation in the average number of days absent in the last year.
   	d.	None of the above is correct.

Answer 1

Answer:

d.None of the above is correct

Reason: In question they have asked for the value of R2. They have not asked for the value of Adjusted R2, But all 3 options are given with adjusted R2. Hence all options are wrong.

Note:

R2=0.248194 = 0.25 rounded to 2 decimals

If we consider about R2 only and not about adusted R2, then correct interpretation will be :

The R2 value is 0.25. This means that the model explains around 25% of the variation in the average number of days absent in the last year.

That is option 'a' without the word adjusted.