An investigator wants to use a straight line to predict IQ from number of words
ID: 3160587 • Letter: A
Question
An investigator wants to use a straight line to predict IQ from number of words in the vocabulary, for a representative group of children aged 2-5. There is some positive association in the data. State whether the following are True or False. Explain your answer for both True and False.
(a) He can use many different lines.
(b) He must use the regression line.
(c) Only the regression line has an r.m.s. error.
(d) Any line he uses will have r.m.s. error.
(e) Among all lines, the regression line will have the smallest r.m.s. error.
Explanation / Answer
(a) He can use many different lines.
False , He should use least square regression line.
(b) He must use the regression line.
True
(c) Only the regression line has an r.m.s. error.
False. To calculate the r.m.s. error, we first need to determine the residuals. Residuals are the difference between the observed values and the predicted values predicted by line.
(d) Any line he uses will have r.m.s. error.
True
(e) Among all lines, the regression line will have the smallest r.m.s. error
True
Regression line minimizes the r.m.s error.
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