The Iowa Tests of Educational Development Are Given Each Year

question 3

Essay

The Iowa Tests of Educational Development are given each year to students around the country. Let x = the previous year's science scores and y = the current year's science scores for a sample of current sophomores who took the test both years. b = estimated slope of the regression line = 0.93 a = estimated y intercept of the regression line = 30.36 ​
a) What is the equation of the estimated regression line?
b) On the graph below, sketch the estimated regression line using the information above. Be sure to label and scale your axes correctly.
c) For students with a score of 250 the previous year, what is the predicted score for the current year?
d) What is the average difference in science score that is associated with a 10-point difference in the previous year's science score?
e) The value of r² is 0.71; interpret r² in the context of this problem.
f) The value of s_e is 25.5. Interpret s_e in the context of this problem.

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Definitions:

Genetic Linkage Studies

Studies in which researchers examine families that have a high incidence of a particular psychiatric disorder. Within these extended families the researchers look for the presence of particular traits (called genetic markers) that can be linked to the occurrence of the disorder.

Psychiatric Disorder

A mental disorder or illness that significantly interferes with an individual’s cognitive, emotional, or social abilities, often diagnosed and treated within the field of psychiatry.

Genetic Markers

Specific sequences of DNA or RNA that can be used to identify individuals or species and are often used to study the relationship between an inherited disease and its genetic cause.

Extended Families

A family structure that goes beyond the nuclear family, including relatives such as grandparents, aunts, uncles, and cousins, often living close to or with each other.