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.

Calculate the t statistic for each slope, at significance level = 0.01.
Dependent Variable R2 Estimated Std. t calculated p-value Differ from 0?
Slope Error
Highest grade achieved .061 −0.027 0.009 .008 No / Yes
Reading grade equivalent .121 −0.070 0.018 .000 No / Yes
Class standing .039 −0.006 0.003 .048 No / Yes
Absence from school .071 4.8 1.7 .006 No / Yes
Grammatical reasoning .051 0.159 0.062 .012 Yes / No
Vocabulary .108 −0.124 0.032 .000 No / Yes
Hand-eye coordination .043 0.041 0.018 .020 No / Yes
Reaction time .025 11.8 6.66 .080 No / Yes
Minor antisocial behavior .025 −0.639 0.36 .082 Yes / No
B) It would be inappropriate to assume cause and effect without a better understanding of how the study was conducted.
1. No
2. Yes

Answer 1

Explanation:

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.

Calculate the t statistic for each slope, at significance level = 0.01.

Dependent Variable R2 Estimated Std. t calculated p-value Differ from 0?

Slope Error

Highest grade achieved .061 −0.027 0.009 .008 No / Yes

Reading grade equivalent .121 −0.070 0.018 .000 No / Yes

Class standing .039 −0.006 0.003 .048 No / Yes

Absence from school .071 4.8 1.7 .006 No / Yes

Grammatical reasoning .051 0.159 0.062 .012 Yes / No

Vocabulary .108 −0.124 0.032 .000 No / Yes

Hand-eye coordination .043 0.041 0.018 .020 No / Yes

Reaction time .025 11.8 6.66 .080 No / Yes

Minor antisocial behavior .025 −0.639 0.36 .082 Yes / No

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

1. No

2. Yes

solution

`t=\frac{\text {estimated slope}}{\text {std error}}`

a)

Estimated Slope Std error t - calculated

-0.027 0.009 -3

-0.070 0.018 -3.89

-0.006 0.003 -2

4.8 1.7 2.82

0.159 0.062 2.56

-0.124 0.032 -3.87

0.041 0.018 2.28

11.8 6.66 1.77

-0.639 0.36 -1.78

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