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:

Incremental Manufacturing Cost

The additional cost incurred to produce an additional unit of a product.

Production Increase

An increment in the amount of products manufactured by a company during a specified period.

Differential Cost

The difference in total cost that will result from selecting one alternative over another in decision-making.

Product Costs

Costs that are directly associated with the production of goods or services, including direct materials, direct labor, and manufacturing overhead.