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, at significance level = 0.01. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
  

Dependent Variable	R2			Estimated Slope			Std. Error			tcalculated	p-value			Differ from 0?
Highest grade achieved		.061			−0.027			0.009				.008		(Click to select)  Yes  No
Reading grade equivalent		.121			−0.070			0.018				.000		(Click to select)  No  Yes
Class standing		.039			−0.006			0.003				.048		(Click to select)  No  Yes
Absence from school		.071			4.8			1.7				.006		(Click to select)  Yes  No
Grammatical reasoning		.051			0.159			0.062				.012		(Click to select)  Yes  No
Vocabulary		.108			−0.124			0.032				.000		(Click to select)  No  Yes
Hand-eye coordination		.043			0.041			0.018				.020		(Click to select)  Yes  No
Reaction time		.025			11.8			6.66				.080		(Click to select)  Yes  No
Minor antisocial behavior		.025			−0.639			0.36				.082		(Click to select)  Yes  No

Answer 1

Concept

Solution

Arranging the data in the proper format

Dependent Variable	R-square	Estimated slope	Std. Error	t-calculated
Highest grade achieved	0.061	-0.027	0.009
Reading grade equivalent	0.121	-0.070	0.018
Class standing	0.039	-0.006	0.003
Absence from School	0.071	4.800	1.700
Grammatical reasoning	0.051	0.159	0.062
Vocabulary	0.108	-0.124	0.032
Hand-eye coordination	0.043	0.041	0.018
Reaction time	0.025	11.800	6.660
Minor antisocial behavior	0.025	-0.639	0.360

R-sq is less than or equal to 1 and positive, so the first column hast to be R-square

Estimated slope and std. error is needed to calculate t-statistic, so based on this information I have populated the table.

Now,

t-statistic for slopes = Estimatd slope / std. error

Calculating t-statistic for each slope as in the table

Dependent Variable	R-square	Estimated slope	Std. Error	t-statistic
Highest grade achieved	0.061	-0.027	0.009	-0.027/0.009 =  -3.00
Reading grade equivalent	0.121	-0.070	0.018	-0.070/0.018 =  -3.89
Class standing	0.039	-0.006	0.003	-0.006/0.003 =  -2.00
Absence from School	0.071	4.800	1.700	4.800/1.700 = 2.82
Grammatical reasoning	0.051	0.159	0.062	0.159/0.062 = 2.56
Vocabulary	0.108	-0.124	0.032	-0.124/0.032 = -3.88
Hand-eye coordination	0.043	0.041	0.018	0.041/0.018 = 2.28
Reaction time	0.025	11.800	6.660	11.8/6.6 = 1.77
Minor antisocial behavior	0.025	-0.639	0.360	-0.639/0.36 =  -1.78