The Iowa Tests of Educational Development Are Given Each Year

question 8

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
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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:

Menstrual Cycle

The monthly series of changes a woman's body goes through in preparation for the possibility of pregnancy.

Depression

An emotional health issue characterized by a consistent feeling of melancholy or a diminished pleasure in tasks, leading to substantial difficulties in daily activities.

Adolescence

The transitional stage of physical and psychological development that generally occurs during the period from puberty to legal adulthood.

Social Relationships

The connections and interactions between individuals or groups, shaping behaviors, attitudes, and social structures.