Crawling Researchers at the University of Denver Infant Study Center $R ^ { 2 }$

question 53

Essay

Crawling Researchers at the University of Denver Infant Study Center investigated
whether babies take longer to learn to crawl in cold months (when they are often bundled
in clothes that restrict their movement) than in warmer months. The study sought an
association between babies' first crawling age (in weeks) and the average temperature
during the month they first try to crawl (about 6 months after birth). Between 1988 and
1991 parents reported the birth month and age at which their child was first able to creep
or crawl a distance of four feet in one minute. Data were collected on 208 boys and 206
girls. The graph below plots average crawling ages (in weeks) against the mean
temperatures when the babies were 6 months old. The researchers found a correlation of r
= -0.70 and their line of best fit was
a. Draw the line of best fit on the graph. (Show your method clearly.)
b. Describe the association in context.
c. Explain (in context) what the slope of the line means.
d. Explain (in context) what the y-intercept of the line means.
e. Explain (in context) what $R ^ { 2 }$
means.
f. In this context, what does a negative residual indicate?

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Definitions:

Pure Monopoly

A market structure where only one supplier provides a unique product or service, thereby controlling the entire market.

Profit-maximizing Price

The price at which a firm can sell its product to earn the highest possible profit, considering its cost structure and market demand.

Regulatory Commission

A government body responsible for enforcing specific laws and regulations covering economic and social policy areas.

Nondiscriminating

Fair treatment not based on preconceived biases or prejudices.