## Hierarchical multiple regression, Mathematics

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A group of children who lived near a lead smelter in El Paso, Texas, were identified and their blood levels of lead were measured. An exposed group of 46 children were identified who had blood-lead levels ≥ 40 μg/mL in 1972 (or for a few children in 1973). This exposed group is defined by the variable Group=2. A control group of 78 children were also identified who had blood-lead levels < 40 μg/mL in both 1972 and 1973. This group is defined by the variable Group=1. All children lived close to the lead smelter. The codebook for this case study is attached in Appendix I.

One important outcome variable studied was IQ. There were three IQ variables measured: IQV (verbal IQ), IQP (performance IQ) and IQF (full scale IQ, not sum or average of IQV and IQP). The other variables including gender (sex), age, distance from the smelter (area), blood lead values in 1972 and 1973 (LD72 and LD 73, FST2YRS (Did child live for 1st 2 years within 1 mile of the smelter) and TOTYRS (Total number of years spent within 4.1 miles of the smelter) were also investigated in the study.

(1) Generate appropriate descriptive statistics to summarise all variables between exposed and control groups; and explain the results. (Charts can be optionally used to support your analysis).

(2) Use t-tests or chi-square tests to compare the differences in age, sex, area, FST2YRS, TOTYRS between exposed and control groups. Present your hypothesis for each test and explain the results.

(3) To explore the relationship between lead exposure and the outcome variables, you need to compare the three outcome variables between exposed group and control group.  Find out if higher lead exposure has significant impacts on the scores of different IQ tests.

(4) Conduct a hierarchical multiple regression to explore factors that impact on children's blood lead level. Enter demographic variables (sex and age) in the first block, and area, FST2YRS and TOTYRS in the second block. Present and interpret your results.

(5) Summarise the major findings you obtained above and discuss the relationship between exposure and outcomes as well as the other contributing factors.

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