Question

Simple regression was employed to establish the effects of childhood exposure to lead. The effective sample size was about 122 subjects. The independent variable was the level of dentin lead (parts per million). Below are regressions using various dependent variables.

    

(a)	Calculate the t statistic for each slope. From the p-values, which slopes differ from zero at α = .01? (Round your answers to 2 decimal places. Negative values should be indicated by a minus sign.)

  

Dependent Variable	R2	Estimated Slope	Std Error	tcalculated	p-value	Differ from 0?
Highest grade achieved	0.095	-0.032	0.002	?	0.000	(Click to select)   Yes   No
Reading grade equivalent	0.167	-0.097	0.023	?	0.000	(Click to select)   No   Yes
Class standing	0.057	-0.007	0.024	?	0.771	(Click to select)   No   Yes
Absence from school	0.070	2.600	1.780	?	0.147	(Click to select)   Yes   No
Grammatical reasoning	0.061	0.196	0.071	?	0.007	(Click to select)   No   Yes
Vocabulary	0.112	-0.114	0.041	?	0.006	(Click to select)   No   Yes
Hand-eye coordination	0.061	0.047	0.035	?	0.182	(Click to select)   Yes   No
Reaction time	0.017	11.200	5.820	?	0.057	(Click to select)   No   Yes
Minor antisocial behavior	0.019	-0.507	0.750	?	0.500	(Click to select)   No   Yes

   

(b)	It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.
	Yes No

Answer 1

Que.a

Formula for calculating t statistic is,

Using this formula we compute t statistic fr all variables.

1. For  Highest grade achieved :

t calculated = -0.032 / 0.002 = -16

Since p-value is less that 0.01, it is differ from zero.

2. Reading grade equivalent :

t calculated = -4.22

Since p-value is less that 0.01, it is differ from zero.

3.  Class standing :

t calculated = -0.29

Since p-value is greater than 0.01, it is not differ from zero.

4. Absence from school :

t calculated = 1.46

Since p-value is greater than 0.01, it is not differ from zero.

5. Grammatical reasoning :

t calculated = 2.76

Since p-value is less that 0.01, it is differ from zero.

6. Vocabulary :

t calculated = -2.78

Since p-value is less that 0.01, it is differ from zero.

7.   Hand-eye coordination:

t calculated = 1.34

Since p-value is greater than 0.01, it is not differ from zero.

8. Reaction time :

t calculated = 1.92

Since p-value is greater than 0.01, it is not differ from zero.

9.  Minor antisocial behavior :

t calculated = -0.676

Since p-value is greater than 0.01, it is not differ from zero.

Que. b

Yes, It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.