The Iowa Tests of Educational Development Are Given Each Year

question 20

Essay

The Iowa Tests of Educational Development are given each year to students around the country. Let x = the previous year's math scores and y = the current year's math scores for a sample of current sophomores who took the test both years. b = estimated slopw of the regression line = 0.9 a = estimated y intercept of the regression line = 35.0 ​
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 a 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 math score that is associated with a 10-point difference in the previous year's math score?
e) The value of r² is 0.74; interpret r² in the context of this problem.
f) The value of s_e is 20.5. Interpret s_e in the context of this problem.

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Definitions:

Personality

A combination of characteristics or qualities that form an individual's distinctive character, influencing behaviors, thoughts, and emotions.

Distinctive Pattern

A unique or characteristic arrangement or sequence that sets something apart from others.

Behaviors

The actions or reactions of an individual or system in response to external or internal stimuli.

Archetype

A universally recognized symbol or character that recurs across cultures and literature, embodying typical patterns of human nature and experience.