Stats 1045 HW 12

An investigator wants to use a straight line to predict IQ from lead levels in the blood, for a representative group of children aged 5-9. There is a weak positive association in the data. True or false: Only the regression line has an r.m.s. error.

False

An investigator wants to use a straight line to predict IQ from lead levels in the blood, for a representative group of children aged 5-9. There is a weak positive association in the data. True or false: He has to use the regression line.

False

An investigator wants to use a straight line to predict IQ from lead levels in the blood, for a representative group of children aged 5-9. There is a weak positive association in the data. True or false: Among all the lines, the regression line has the smallest r.m.s. error.

True

For men age 18-24 in the HANES5 sample, the regression equation for predicting height from weight is predicted height = (0.0267 inches per pound) * (weight) + 65.2 inches (Height is measured in inches and weight in pounds.) If someone puts on 20 pounds, will he get taller by (20 pounds) * (0.0267 inches per pound) = 0.5 inches? If not what does the slope mean?

No, the slope means that men one pound heavier are taller, on average, by about 0.0267 inches.

An investigator wants to use a straight line to predict IQ from lead levels in the blood, for a representative group of children aged 5-9. There is a weak positive association in the data. True or false: He can use many different lines.

True

A congressional report is discussing the relationship between income of parents and educational attainment of their daughters. Data are from a sample of families with daughters age 18-24. Average parental income is $79,300; average educational attainment of the daughters is 12.7 years of schooling completed; the correlation is 0.37. The regression line for predicting daughter's education from parental income is reported as y = mx + b, with x = parental income (dollars), y = predicted education (years), m = 0.00000925 years per dollar, and b = 10.3 years: predicted\:education\:=\:0.00000925\times income+10.3 p r e d i c t e d e d u c a t i o n = 0.00000925 × i n c o m e + 10.3 Is anything wrong? Or do you need more information to decide?

Yes, the regression line has to go through the point of averages and this line doesn't.

In a large study of the relationship between parental income and the IQs of their children, the following results were obtained: average income = $90,000, SD = $45,000 average IQ = 100, SD = 15, r = 0.50 For each income group ($0-$9999, $10,000-$19,999, $20,000-$29,999, etc.), the average IQ of children with parental income in that group was calculated and then plotted above the midpoint of the group ($5,000, $15,000, $25,000, etc.). It was found that the points on this graph followed a straight line very closely. One child in the study referred to above had an IQ of 110, but the information about his parents' income was lost. At $150,000 the height of the line plotted as described above corresponds to an IQ of 110. Is $150,000:

too high for the parents' income; you need to use the other regression line, for predicting parents' income from child's IQ.